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Page 7383 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
Iarrobino, Jr. (1-NORE; Boston, MA) 99k:14008 14C05 06A07 13P10 Mall, Daniel (CH-ETHZ; Ziirich) Characterisations of lexicographic sets and simply-connected Hilbert schemes.  ...  The author applies these results to give a combinatorial proof that some Hilbert schemes which were given by G. Gotzmann [Math. Z. 180 (1982), no. 3, 291-305; MR 84c:14003] are simply connected.  ... 

Computing spin networks

Annalisa Marzuoli, Mario Rasetti
2005 Annals of Physics  
The model proposed can be thought of as the non-Boolean generalization of the quantum circuit model, with unitary gates expressed in terms of 3nj coefficients connecting inequivalent binary coupling schemes  ...  We expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands.  ...  Carfora also for his unexhaustible enthusiasm in helping us with the preparation of all figures, and with V. Aquilanti and C. Coletti for the permission to reproduce Fig. 21 from [27] .  ... 
doi:10.1016/j.aop.2005.01.005 fatcat:4n3izo3ozfdcbozh7bzapvbcya

The Hilbert scheme of points and its link with border basis [article]

Mariemi Alonso , Bernard Mourrain
2010 arXiv   pre-print
This new explicit description of the Hilbert scheme is simpler than the previous ones and global. It involves equations of degree 2.  ...  Next, we consider infinitesimal perturbations of an input system of equations on this Hilbert scheme and describe its tangent space.  ...  of the punctual Hilbert scheme and deduce an explicit representation of the Hilbert functor.  ... 
arXiv:0911.3503v2 fatcat:bdqzsnnn4rgefeg37z7ybt6avm

On moduli spaces of sheaves on K3 or abelian surfaces [article]

Markus Zowislok
2011 arXiv   pre-print
and over components of many of the moduli spaces of two-dimensional sheaves on K3 surfaces, in particular, of those for rank two sheaves.  ...  We investigate the moduli spaces of one- and two-dimensional sheaves on projective K3 and abelian surfaces that are semistable with respect to a nongeneral ample divisor with regard to the symplectic resolvability  ...  For a k-scheme S let M ′ (S) be the set of all isomorphism classes of S-flat families of (H, A)-semistable sheaves on X with Hilbert polynomial P with respect to H, and for a k-morphism f : According to  ... 
arXiv:1104.5629v1 fatcat:gq3hmzuh4fgprowgwpzj3n75j4

A functorial construction of moduli of sheaves

Luis Álvarez-Cónsul, Alastair King
2007 Inventiones Mathematicae  
We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves.  ...  This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.  ...  An important set of invariants of X are the projective schemes M ss X (P ), which are the moduli spaces for semistable coherent sheaves of O X -modules with fixed Hilbert polynomial P , with respect to  ... 
doi:10.1007/s00222-007-0042-5 fatcat:7xtv5ng52zhtzahm2huqiegdpi

Apolarity, border rank and multigraded Hilbert scheme [article]

Weronika Buczyńska, Jarosław Buczyński
2020 arXiv   pre-print
A critical ingredient of our work is an irreducible component of a multigraded Hilbert scheme related to the toric variety in question.  ...  We also define a border rank version of the variety of sums of powers and analyse its usefulness in studying tensors and polynomials with large symmetries.  ...  We are grateful to the authors of [CHL19] for sharing the subsequent versions of their results and the initial drafts of the article.  ... 
arXiv:1910.01944v2 fatcat:xtmmlsxz3jaa5odstf7mulktmu

Operational Quantum Logic: An Overview [chapter]

Bob Coecke, David Moore, Alexander Wilce
2000 Current Research in Operational Quantum Logic  
Consequently, there is a particular focus in this paper on the (survey) articles of that volume, which are dedicated to D.J.  ...  Foulis in honor of his seminal contributions to our field. 2 The author is Postdoctoral Researcher at Flanders' Fund for Scientific Reseach.  ...  of ortholattices where the set of complements of any given element may be simply computed.  ... 
doi:10.1007/978-94-017-1201-9_1 fatcat:ubb4ku7xhfb5nfv6nrjm7jujza

Operational quantum logic: An overview [article]

Bob Coecke, David Moore, Alexander Wilce
2001 arXiv   pre-print
To orient readers new to this subject, we shall recount some of the historical development of quantum logic, attempting to show how the physical and mathematical sides of the subject have influenced and  ...  Our aim here is to give a uniform presentation of what we call operational quantum logic, highlighting both its concrete physical origins and its purely mathematical structure.  ...  of ortholattices where the set of complements of any given element may be simply computed.  ... 
arXiv:quant-ph/0008019v2 fatcat:d3ovzfpkx5afze6qe724mtv5te

A diagrammatic calculus of fermionic quantum circuits [article]

Giovanni de Felice, Amar Hadzihasanovic, Kang Feng Ng
2019 arXiv   pre-print
the parity of states, and the tensor product as monoidal product.  ...  After defining a fermionic circuit model, we present the basic components of the calculus, together with their interpretation, and show how the main physical gates of interest in FQC can be represented  ...  , lexicographic) on n-tuples of bits to make this unique.  ... 
arXiv:1801.01231v4 fatcat:s5hq74tsqbeyfj7yjbs6dlvuly

Spatial logic of tangled closure operators and modal mu-calculus

Robert Goldblatt, Ian Hodkinson
2017 Annals of Pure and Applied Logic  
We also show that in the presence of ∀, strong completeness fails if X is compact and locally connected.  ...  There has been renewed interest in recent years in McKinsey and Tarski's interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric  ...  The second author thanks the School of Mathematics and Statistics at Victoria University of Wellington for their warm and generous hospitality during his visit in January-March 2014 when the authors worked  ... 
doi:10.1016/j.apal.2016.11.006 fatcat:dcdjhcojfzh47fgixf2fqxlktu

Geometric Reid's recipe for dimer models [article]

Raf Bocklandt, Alastair Craw, Alexander Quintero Velez
2014 arXiv   pre-print
By choosing a special stability parameter and hence a distinguished crepant resolution Y, this derived equivalence generalises the Fourier-Mukai transform relating the G-Hilbert scheme and the skew group  ...  This generalises results of Cautis-Logvinenko and Cautis-Craw-Logvinenko to the dimer setting, though our approach is different in each case.  ...  resolution of C 3 /G, namely the G-Hilbert scheme Y = G -Hilb(C 3 ).  ... 
arXiv:1305.0156v2 fatcat:2jpwwafaarai7bxhw3frqvuaou

Geometric Reid's recipe for dimer models

Raf Bocklandt, Alastair Craw, Alexander Quintero Vélez
2014 Mathematische Annalen  
By choosing a special stability parameter and hence a distinguished crepant resolution Y , this derived equivalence generalises the Fourier-Mukai transform relating the G-Hilbert scheme and the skew group  ...  This generalises results of Cautis-Logvinenko [7] and Cautis-Craw-Logvinenko [6] to the dimer setting, though our approach is different in each case.  ...  resolution of C 3 /G, namely the G-Hilbert scheme Y = G -Hilb(C 3 ).  ... 
doi:10.1007/s00208-014-1085-8 fatcat:grwhyp2yh5boberlvgdzcdzaze

GEOMETRIC WEIGHT-SHIFTING OPERATORS ON HILBERT MODULAR FORMS IN CHARACTERISTIC p

Fred Diamond
2021 Journal of the Institute of Mathematics of Jussieu  
In particular, we use the partial Hasse invariants and Kodaira–Spencer filtrations defined by Reduzzi and Xiao to improve on Andreatta and Goren's construction of partial $\Theta $ -operators, obtaining  ...  Finally, we apply our results to prove a partial positivity result for minimal weights of mod p Hilbert modular forms.  ...  Recall that the q-expansion principle allows one to characterise Hilbert modular forms in terms of their q-expansions. Proposition 7.2.2.  ... 
doi:10.1017/s1474748021000530 fatcat:ewcoj5xcwzg4tcnfud74w6o7pa

The algebra of entanglement and the geometry of composition [article]

Amar Hadzihasanovic
2017 arXiv   pre-print
We re-evaluate the category of Hilbert spaces from the perspective of categorical universal algebra, which leads to a bicategorical refinement.  ...  We conclude with generalisations of the ZW calculus to higher-dimensional systems, including the definition of a universal set of generators in each dimension.  ...  (2.1), and nat f c of diagram (2.2) still escape this characterisation.  ... 
arXiv:1709.08086v2 fatcat:ts5oz4iqsnaonfk4m2damc7jyq

A minimal approach to the scattering of physical massless bosons

Rutger H. Boels, Hui Luo
2018 Journal of High Energy Physics  
Several interesting features of the results are highlighted, such as the vanishing of certain basis coefficients for gluon and graviton amplitudes.  ...  These include the planar four point two-loop amplitude in pure Yang-Mills theory as well as a range of one loop amplitudes with internal and external scalars, gluons and gravitons.  ...  This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s)  ... 
doi:10.1007/jhep05(2018)063 fatcat:bb5csko7kbcfvaxaa25q2kup4u
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