IA Scholar Query: A mapping-independent primitive for the triangulation of parametric surfaces.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgMon, 21 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Geometric Model Checking of Continuous Space
https://scholar.archive.org/work/ppfkmlutkna2jae77ifet2ccaa
Topological Spatial Model Checking is a recent paradigm where model checking techniques are developed for the topological interpretation of Modal Logic. The Spatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachability connectives that, in turn, can be used for expressing interesting spatial properties, such as "being near to" or "being surrounded by". SLCS constitutes the kernel of a solid logical framework for reasoning about discrete space, such as graphs and digital images, interpreted as quasi discrete closure spaces. Following a recently developed geometric semantics of Modal Logic, we propose an interpretation of SLCS in continuous space, admitting a geometric spatial model checking procedure, by resorting to models based on polyhedra. Such representations of space are increasingly relevant in many domains of application, due to recent developments of 3D scanning and visualisation techniques that exploit mesh processing. We introduce PolyLogicA, a geometric spatial model checker for SLCS formulas on polyhedra and demonstrate feasibility of our approach on two 3D polyhedral models of realistic size. Finally, we introduce a geometric definition of bisimilarity, proving that it characterises logical equivalence.Nick Bezhanishvili and Vincenzo Ciancia and David Gabelaia and Gianluca Grilletti and Diego Latella and Mieke Massinkwork_ppfkmlutkna2jae77ifet2ccaaMon, 21 Nov 2022 00:00:00 GMTHomotopic curve shortening and the affine curve-shortening flow
https://scholar.archive.org/work/flm5k5ehhvhi7bsowlsl4sk7su
We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call "homotopic curve shortening" (HCS), starts with a closed curve (which might self-intersect) in the presence of a set P⊂ℝ^2 of point obstacles, and evolves in discrete steps, where each step consists of (1) taking shortcuts around the obstacles, and (2) reducing the curve to its shortest homotopic equivalent. We find experimentally that, if the initial curve is held fixed and P is chosen to be either a very fine regular grid or a uniformly random point set, then HCS behaves at the limit like the affine curve-shortening flow (ACSF). This connection between ACSF and HCS generalizes the link between ACSF and convex-layer decomposition (Eppstein et al., 2017; Calder and Smart, 2020), which is restricted to convex curves. We prove that HCS satisfies some properties analogous to those of ACSF: HCS is invariant under affine transformations, preserves convexity, and does not increase the total absolute curvature. Furthermore, the number of self-intersections of a curve, or intersections between two curves (appropriately defined), does not increase. Finally, if the initial curve is simple, then the number of inflection points (appropriately defined) does not increase.Sergey Avvakumov, Gabriel Nivaschwork_flm5k5ehhvhi7bsowlsl4sk7suMon, 14 Nov 2022 00:00:00 GMTLinking numbers of modular knots
https://scholar.archive.org/work/5fmj52rzh5gifnfjwqjcwafy7y
The modular group PSL(2;Z) acts on the hyperbolic plane HP with quotient the modular surface M, whose unit tangent bundle U is a 3-manifold homeomorphic to the complement of the trefoil knot in the 3-sphere. The hyperbolic conjugacy classes of PSL(2;Z) correspond to the closed oriented geodesics in M. Those lift to the periodic orbits for the geodesic flow in U, which define the modular knots. The linking numbers between modular knots and the trefoil is well understood. Indeed, Etienne Ghys showed in 2006 that they are given by the Rademacher invariant of the corresponding conjugacy classes. The Rademacher function is a homogeneous quasi-morphism of PSL(2;Z) which he had recognised with Jean Barge in 1992 as half the primitive of the bounded euler class. This shed light on the 1987 work of Michael Atiyah concerning the logarithm of the Dedekind eta function which identified it with no less than that six other important functions appearing in diverse areas of mathematics. We are concerned with the linking numbers between modular knots and derive several formulae with arithmetical, combinatorial, topological and group theoretical flavours. In particular we associate to a pair of modular knots a function defined on the character variety of PSL(2;Z), whose limit at the boundary point recovers their linking number. Moreover, we show that the linking number with a modular knot minus that with its inverse yields a homogeneous quasi-morphism on the modular group, and how to extract a free basis out of these. For this we prove that the linking pairing is non degenerate.Christopher-Lloyd Simonwork_5fmj52rzh5gifnfjwqjcwafy7yFri, 11 Nov 2022 00:00:00 GMTThe Asymptotic Weak Gravity Conjecture for Open Strings
https://scholar.archive.org/work/b2sbhlqxavfh3g6s6vjqdyacsu
We investigate the asymptotic Tower Weak Gravity Conjecture in weak coupling limits of open string theories with minimal supersymmetry in four dimensions, focusing for definiteness on gauge theories realized on 7-branes in F-theory. Contrary to expectations, we find that not all weak coupling limits contain an obvious candidate for a tower of states marginally satisfying the super-extremality bound. The weak coupling limits are classified geometrically in the framework of EFT string limits and their generalizations. We find three different classes of weak coupling limits, whose physics is characterized by the ratio of the magnetic weak gravity scale and the species scale. The four-dimensional Tower Weak Gravity Conjecture is satisfied by the (non-BPS) excitations of the weakly coupled EFT string only in emergent string limits, where the EFT string can be identified with a critical (heterotic) string. All other weak coupling limits lead to a decompactification either to an in general strongly coupled gauge theory coupled to gravity or to a defect gauge theory decoupling from the gravitational bulk, in agreement with the absence of an obvious candidate for a marginally super-extremal tower of states.Cesar Fierro Cota, Alessandro Mininno, Timo Weigand, Max Wiesnerwork_b2sbhlqxavfh3g6s6vjqdyacsuThu, 10 Nov 2022 00:00:00 GMTFibre-reinforced additive manufacturing: from design guidelines to advanced lattice structures
https://scholar.archive.org/work/yiy7lwmscvh4hkgcou5lc54uly
In pursuit of achieving ultimate lightweight designs with additive manufacturing (AM), engineers across industries are increasingly gravitating towards composites and architected cellular solids; more precisely, fibre-reinforced polymers and functionally graded lattices (FGLs). Control over material anisotropy and the cell topology in design for AM (DfAM) offer immense scope for customising a part's properties and for the efficient use of material. This research expands the knowledge on the design with fibre-reinforced AM (FRAM) and the elastic-plastic performance of FGLs. Novel toolpath strategies, design guidelines and assessment criteria for FRAM were developed. For this purpose, an open-source solution was proposed, successfully overcoming the limitations of commercial printers. The effect of infill patterns on structural performance, economy, and manufacturability was examined. It was demonstrated how print paths informed by stress trajectories and key geometric features can outperform conventional patterns, laying the groundwork for more sophisticated process planning. A compilation of the first comprehensive database on fibre-reinforced FGLs provided insights into the effect of grading on the elastic performance and energy absorption capability, subject to strut-and surface-based lattices, build direction and fibre volume fraction. It was elucidated how grading the unit cell density within a lattice offers the possibility of tailoring the stiffness and achieving higher energy absorption than ungraded lattices. Vice versa, grading the unit cell size of lattices yielded no effect on the performance and is thus exclusively governed by the density. These findings help exploit the lightweight potential of FGLs through better informed DfAM. A new and efficient methodology for predicting the elastic-plastic characteristics of FGLs under large strain deformation, assuming homogenised material properties, was presented. A phenomenological constitutive model that was calibrated based upon interpolated material data [...]János Plocher, Ajit Panesar, Vito Tagarielli, Engineering And Physical Sciences Research Councilwork_yiy7lwmscvh4hkgcou5lc54ulyThu, 10 Nov 2022 00:00:00 GMTTurbulence as Clebsch Confinement
https://scholar.archive.org/work/qrlmjshh65cfddfvw4x3lbhb44
We argue that in the strong turbulence phase, as opposed to the weak one, the Clebsch variables compactify to the sphere S_2 and are not observable as wave excitations. Various topologically nontrivial configurations of this confined Clebsch field are responsible for vortex sheets. Stability equations (CVS) for closed vortex surfaces (bubbles of Clebsch field) are derived and investigated. The exact non-compact solution for the stable vortex sheet family is presented. Compact solutions are proven not to exist by De Lellis and Brué. Asymptotic conservation of anomalous dissipation on stable vortex surfaces in the turbulent limit is discovered. We derive an exact formula for this anomalous dissipation as a surface integral of the square of velocity gap times the square root of minus local normal strain. Topologically stable time-dependent solutions, which we call Kelvinons, are introduced. They have a conserved velocity circulation around static loop; this makes them responsible for asymptotic PDF tails of velocity circulation, perfectly matching numerical simulations. The loop equation for circulation PDF as functional of the loop shape is derived and studied. This equation is exactly equivalent to the Schrödinger equation in loop space, with viscosity ν playing the role of Planck's constant. This equivalence opens the way for direct numerical simulation of turbulence on quantum computers. Kelvinons are fixed points of the loop equation at turbulent limit ν→ 0. Area law and the asymptotic scaling law for mean circulation at a large area are derived. The representation of the solution of the loop equation in terms of a singular stochastic equation for momentum loop trajectory is presented.Alexander Migdalwork_qrlmjshh65cfddfvw4x3lbhb44Mon, 07 Nov 2022 00:00:00 GMTDimer model and holomorphic functions on t-embeddings of planar graphs
https://scholar.archive.org/work/x4m42h6fufdnrop35qdrlpngty
We introduce the framework of discrete holomorphic functions on t-embeddings of weighted bipartite planar graphs; t-embeddings also appeared under the name Coulomb gauges in a recent paper arXiv:1810.05616. We argue that this framework is particularly relevant for the analysis of scaling limits of the height fluctuations in the corresponding dimer models. In particular, it unifies both Kenyon's interpretation of dimer observables as derivatives of harmonic functions on T-graphs and the notion of s-holomorphic functions originated in Smirnov's work on the critical Ising model. We develop an a priori regularity theory for such functions and provide a meta-theorem on convergence of the height fluctuations to the Gaussian Free Field. We also discuss how several more standard discretizations of complex analysis fit this general framework.Dmitry Chelkak, Benoît Laslier, Marianna Russkikhwork_x4m42h6fufdnrop35qdrlpngtyMon, 07 Nov 2022 00:00:00 GMTOn the intermediate Jacobian of M5-branes
https://scholar.archive.org/work/egrpd2pouzgntmwtuahkm66wwi
We study Euclidean M5-branes wrapping vertical divisors in elliptic Calabi-Yau fourfold compactifications of M/F-theory that admit a Sen limit. We construct these Calabi-Yau fourfolds as elliptic fibrations over coordinate flip O3/O7 orientifolds of toric hypersurface Calabi-Yau threefolds. We devise a method to analyze the Hodge structure (and hence the dimension of the intermediate Jacobian) of vertical divisors in these fourfolds, using only the data available from a type IIB compactification on the O3/O7 Calabi-Yau orientifold. Our method utilizes simple combinatorial formulae (that we prove) for the equivariant Hodge numbers of the Calabi-Yau orientifolds and their prime toric divisors, along with a formula for the Euler characteristic of vertical divisors in the corresponding elliptic Calabi-Yau fourfold. Our formula for the Euler characteristic includes a conjectured correction term that accounts for the contributions of pointlike terminal ℤ_2 singularities corresponding to perturbative O3-planes. We check our conjecture in a number of explicit examples and find perfect agreement with the results of direct computations.Patrick Jefferson, Manki Kimwork_egrpd2pouzgntmwtuahkm66wwiMon, 07 Nov 2022 00:00:00 GMTDisk potential functions for polygon spaces
https://scholar.archive.org/work/jpio32cjcngsjdbvvhp5xdrvpe
We derive a Floer theoretical SYZ mirror for an equilateral and generic polygon space. The disk potential function of the monotone torus fiber of the caterpillar bending system is calculated by computing non-trivial open Gromov--Witten invariants from the structural result of the monotone Fukaya category, the topology of fibers of completely integrable systems, and toric degenerations. Then, combining the result with the work of Nohara--Ueda [NU20] and Marsh--Rietsch [MR20], we obtain the disk potential functions of bending systems and produce a mirror cluster variety of type A without frozen variables via Lagrangian Floer theory.Yoosik Kim, Siu-Cheong Lau, Xiao Zhengwork_jpio32cjcngsjdbvvhp5xdrvpeMon, 07 Nov 2022 00:00:00 GMTGroups acting on veering pairs and Kleinian groups
https://scholar.archive.org/work/c7loy3vfnzgurow6hcuebgnr4i
We show that some laminar group which has an invariant veering pair of laminations is a hyperbolic 3-orbifold group. On the way, we show that from a veering pair of laminations, one can construct a loom space (in the sense of Schleimer-Segerman) as a quotient. Our approach does not assume the existence of any 3-manifold to begin with so this is a geometrization-type result, and supersedes some of the results regarding the relation among veering triangulations, pseudo-Anosov flows, taut foliations in the literature.Hyungryul Baik, Hongtaek Jung, KyeongRo Kimwork_c7loy3vfnzgurow6hcuebgnr4iMon, 07 Nov 2022 00:00:00 GMTNon-unitary TQFTs from 3D 𝒩=4 rank 0 SCFTs
https://scholar.archive.org/work/yzorlugsxzgatlycsto7bqeuda
We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT_± [𝒯_ rank 0], to a (2+1)D interacting 𝒩=4 superconformal field theory (SCFT) 𝒯_ rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = max_α(- log |S^(+)_0α| ) = max_α(- log |S^(-)_0α|), where F is the round three-sphere free energy of 𝒯_ rank 0 and S^(±)_0α is the first column in the modular S-matrix of TFT_±. From the dictionary, we derive the lower bound on F, F ≥ -log(√(5-√(5)/10)) ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal 𝒩=4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.Dongmin Gang, Sungjoon Kim, Kimyeong Lee, Myungbo Shim, Masahito Yamazakiwork_yzorlugsxzgatlycsto7bqeudaTue, 01 Nov 2022 00:00:00 GMTModular representations of finite groups and Lie theory
https://scholar.archive.org/work/ng7rjnnbrzcq7bwklmrhxxgek4
This article discusses the modular representation theory of finite groups of Lie type from the viewpoint of Broue's abelian defect group conjecture. We discuss both the defining characteristic case, the inspiration for Alperin's weight conjecture, and the non-defining case, the inspiration for Broue's conjecture. The modular representation theory of general finite groups is conjectured to behave both like that of finite groups of Lie type in defining characteristic, and in non-defining characteristic, to a large extent. The expected behaviour of modular representation theory of finite groups of Lie type in defining characteristic is particularly difficult to grasp along the lines of Broue's conjecture and we raise a new question related to the change of central character. We introduce a degeneration method in the modular representation theory of finite groups of Lie type in non-defining characteristic. Combined with the rigidity property of perverse equivalences, this provides a setting for two variable decomposition matrices, for large characteristic. This should help make progress towards finding decomposition matrices, an outstanding problem with few general results beyond the case of general linear groups. This last part is based on joint work with David Craven and Olivier Dudas.Raphael Rouquierwork_ng7rjnnbrzcq7bwklmrhxxgek4Tue, 01 Nov 2022 00:00:00 GMTTowards an exact description of Gravitational Waves with a Positive Cosmological Constant: Basic Framework
https://scholar.archive.org/work/lqv7y7ansrebrkbhoirgnn4f6i
Gravitational waves (GW) are a natural consequence of general relativity (GR), first derived by Einstein in 1918, but their existence was debated as the derivation was only available in the linearized version of the theory. Only in 1960 the existence of GW in full GR was established. The non-trivial task of finding a workable definition for gravitational waves in general relativity was achieved and their existence as a solution to the Einstein equations for vanishing cosmological constant has been proven. But although much work has been done to extend this proof the case of a positive cosmological constant (which is a best fit model of cosmology with current observations) a description in the full non-linear theory is still missing. We take inspiration from the Bondi-Sachs formalism and approach the problem in a novel way, by describing a geometry via geodesics and thus removing the degeneracy between coordinates and the metric. Our formalism uses infinitesimal spherical triangles as geometry generating elements, to relate the geodesic flow bundle to Gaussian curvature. This ultimately allows us to calculate all geodesics from a curvature field up to second order. In this paper we describe the first step of the space-like part of the solution, in which we reduce an n-dimensional problem to a 2-dimensional triangulation problem.Adrian Boitier, Shubhanshu Tiwariwork_lqv7y7ansrebrkbhoirgnn4f6iSat, 29 Oct 2022 00:00:00 GMTState of the Art in Dense Monocular Non-Rigid 3D Reconstruction
https://scholar.archive.org/work/wac7jz7yebhuxfq7hkhdnt74gy
3D reconstruction of deformable (or non-rigid) scenes from a set of monocular 2D image observations is a long-standing and actively researched area of computer vision and graphics. It is an ill-posed inverse problem, since--without additional prior assumptions--it permits infinitely many solutions leading to accurate projection to the input 2D images. Non-rigid reconstruction is a foundational building block for downstream applications like robotics, AR/VR, or visual content creation. The key advantage of using monocular cameras is their omnipresence and availability to the end users as well as their ease of use compared to more sophisticated camera set-ups such as stereo or multi-view systems. This survey focuses on state-of-the-art methods for dense non-rigid 3D reconstruction of various deformable objects and composite scenes from monocular videos or sets of monocular views. It reviews the fundamentals of 3D reconstruction and deformation modeling from 2D image observations. We then start from general methods--that handle arbitrary scenes and make only a few prior assumptions--and proceed towards techniques making stronger assumptions about the observed objects and types of deformations (e.g. human faces, bodies, hands, and animals). A significant part of this STAR is also devoted to classification and a high-level comparison of the methods, as well as an overview of the datasets for training and evaluation of the discussed techniques. We conclude by discussing open challenges in the field and the social aspects associated with the usage of the reviewed methods.Edith Tretschk, Navami Kairanda, Mallikarjun B R, Rishabh Dabral, Adam Kortylewski, Bernhard Egger, Marc Habermann, Pascal Fua, Christian Theobalt, Vladislav Golyanikwork_wac7jz7yebhuxfq7hkhdnt74gyThu, 27 Oct 2022 00:00:00 GMTEvaluations of annular Khovanov–Rozansky homology
https://scholar.archive.org/work/wph7kpmgfbbjhc7kmv2omtp34u
We describe the universal target of annular Khovanov-Rozansky link homology functors as the homotopy category of a free symmetric monoidal category generated by one object and one endomorphism. This categorifies the ring of symmetric functions and admits categorical analogues of plethystic transformations, which we use to characterize the annular invariants of Coxeter braids. Further, we prove the existence of symmetric group actions on the Khovanov-Rozansky invariants of cabled tangles and we introduce spectral sequences that aid in computing the homologies of generalized Hopf links. Finally, we conjecture a characterization of the horizontal traces of Rouquier complexes of Coxeter braids in other types.Eugene Gorsky, Paul Wedrichwork_wph7kpmgfbbjhc7kmv2omtp34uTue, 25 Oct 2022 00:00:00 GMTDirect Immersogeometric Fluid Flow and Heat Transfer Analysis of Objects Represented by Point Clouds
https://scholar.archive.org/work/52dxtym4vbfkbjtolp45qnjxca
Immersogeometric analysis (IMGA) is a geometrically flexible method that enables one to perform multiphysics analysis directly using complex computer-aided design (CAD) models. In this paper, we develop a novel IMGA approach for simulating incompressible and compressible flows around complex geometries represented by point clouds. The point cloud object's geometry is represented using a set of unstructured points in the Euclidean space with (possible) orientation information in the form of surface normals. Due to the absence of topological information in the point cloud model, there are no guarantees for the geometric representation to be watertight or 2-manifold or to have consistent normals. To perform IMGA directly using point cloud geometries, we first develop a method for estimating the inside-outside information and the surface normals directly from the point cloud. We also propose a method to compute the Jacobian determinant for the surface integration (over the point cloud) necessary for the weak enforcement of Dirichlet boundary conditions. We validate these geometric estimation methods by comparing the geometric quantities computed from the point cloud with those obtained from analytical geometry and tessellated CAD models. In this work, we also develop thermal IMGA to simulate heat transfer in the presence of flow over complex geometries. The proposed framework is tested for a wide range of Reynolds and Mach numbers on benchmark problems of geometries represented by point clouds, showing the robustness and accuracy of the method. Finally, we demonstrate the applicability of our approach by performing IMGA on large industrial-scale construction machinery represented using a point cloud of more than 12 million points.Aditya Balu, Manoj R. Rajanna, Joel Khristy, Fei Xu, Adarsh Krishnamurthy, Ming-Chen Hsuwork_52dxtym4vbfkbjtolp45qnjxcaTue, 25 Oct 2022 00:00:00 GMTDiscriminants and toric K-theory
https://scholar.archive.org/work/5w4u2t3buvf7dl2wma4aewcac4
We discuss a categorical approach to the theory of discriminants in the combinatorial language introduced by Gelfand, Kapranov and Zelevinsky. Our point of view is inspired by homological mirror symmetry and provides K–theoretic evidence for a conjecture presented by Paul Aspinwall in a conference talk in Banff in March 2016 and later in a joint paper with Plesser and Wang.R. Paul Horja, Ludmil Katzarkovwork_5w4u2t3buvf7dl2wma4aewcac4Mon, 24 Oct 2022 00:00:00 GMTEntropy and Diversity: The Axiomatic Approach
https://scholar.archive.org/work/3fyneywa4fbufiumyzxnwreqvm
This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question "what is diversity?" has surprising mathematical depth, and breadth too: this book involves parts of mathematics ranging from information theory, functional equations and probability theory to category theory, geometric measure theory and number theory. It applies the power of the axiomatic method to a biological problem of pressing concern, but the new concepts and theorems are also motivated from a purely mathematical perspective. The main narrative thread requires no more than an undergraduate course in analysis. No familiarity with entropy or diversity is assumed.Tom Leinsterwork_3fyneywa4fbufiumyzxnwreqvmSat, 22 Oct 2022 00:00:00 GMTOn Vacuum Structures and Quantum Corrections in String Theory
https://scholar.archive.org/work/26gtp4n6enfwlklbnlwofhzady
A key target for fundamental physics remains developing a clear understanding of ultra-violet (UV) limits of Effective Field Theories (EFTs) coupled to gravity. In this context, string theory has emerged as a viable candidate for a UV complete theory of quantum gravity. Its compactifications result in a landscape of string vacua encompassing an immensely rich and diverse structure of EFTs. Extracting reliable low energy information from string compactifications notoriously requires a systematic derivation of corrections to the tree level actions which remains a key challenge. Further, despite astonishing progress in constructing string solutions, locating realistic string vacua with desirable properties in the landscape proves to be a delicate task. The objectives of this thesis are threefold: I) first, to perform an extensive analysis of quantum corrections in string theory; II) second, to create a systematic framework to study geometries and backgrounds for viable string compactifications; and III) third, to assess the attainable EFTs in the context of moduli stabilisa- tion. The synergy of these strategies constitutes an innovative approach towards addressing phenomenological questions in string theory. The first part of this thesis describes progress in deriving corrections to classi- cal string effective actions from multi-dimensional investigations by employing the powerful machinery of string dualities and symmetries. Initially, we investigate the structure of higher derivative terms involving the 3-form G3 in the α′ and string-loop expansion of the ten-dimensional Type IIB effective action. Subsequently, we ex- plore α′ corrections in F-theory compactifications to four dimensions in Ch. 6. Here, we focus on the moduli dependence of perturbative corrections to scalar potentials by performing a dimensional analysis. The second part concerns the development of new techniques to examine large classes of Calabi-Yau (CY) geometries and realising the Standard Model in string compactifications. In a first step, w [...]Andreas Schachner, Apollo-University Of Cambridge Repository, Fernando Quevedowork_26gtp4n6enfwlklbnlwofhzadyFri, 21 Oct 2022 00:00:00 GMTThe cohomology of spherical vector bundles on K3 surfaces
https://scholar.archive.org/work/vebbgsmsozckri6epei6err4j4
We find an algorithm to compute the cohomology groups of spherical vector bundles on complex projective K3 surfaces, in terms of their Mukai vectors. In many good cases, we give significant simplifications of the algorithm. As an application, when the Picard rank is one, we show a numerical condition that is equivalent to weak Brill-Noether for a spherical vector bundle.Yeqin Liuwork_vebbgsmsozckri6epei6err4j4Thu, 20 Oct 2022 00:00:00 GMT