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Kummer configurations and designs embedded in planes

A.A Bruen
1989 Journal of combinatorial theory. Series A  
Any (16, 6, 2) design isomorphic to the one described above is said to be of grid type. KUMMER CONFIGURATIONS AND DESIGNS Let us summarize some work from [2] .  ...  Our proof consists of exploiting the classical Kummer surface or rather the famous configuration of its 16 singular points and planes which, in fact, form a biplane of grid type (see Sections 2 and 3).  ... 
doi:10.1016/0097-3165(89)90069-1 fatcat:xjb6biuzkze5ld7b7tmxzfvoly

Abstract configurations in algebraic geometry [article]

I. Dolgachev
2003 arXiv   pre-print
In this paper we discuss some examples of abstract configurations and, in particular finite geometries, which one encounters in algebraic geometry.  ...  of elements from the second set and each element of the second set is related to the same number r of elements in the first set.  ...  One can show that this action is isomorphic to the action of W g on the Kummer configuration defined in 10.4. 10.6. The Kummer designs.  ... 
arXiv:math/0304258v1 fatcat:mxje55nd7vgrbpiiam3jmojbq4

Page 3338 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
For example, the Kummer 16¢ configuration is examined in the guise of a set of 16 points and 16 conics such that any two of the conics meet in precisely two of the points.  ...  This leads to a menu of interesting questions on systems of (hyper) ovals in planes of even order, on codes, on 2-designs and on nuclei. {For the entire collection see MR 93m:00039.} J. W. P.  ... 

Computing isogenies between Jacobian of curves of genus 2 and 3 [article]

Enea Milio
2019 arXiv   pre-print
This work is based from the paper "Computing functions on Jacobians and their quotients" of Jean-Marc Couveignes and Tony Ezome.  ...  We present a quasi-linear algorithm to compute isogenies between Jacobians of curves of genus 2 and 3 starting from the equation of the curve and a maximal isotropic subgroup of the l-torsion, for l an  ...  I thank Pierrick Gaudry for suggesting me to work on [10] , for helping me in my first footsteps and for giving me the idea of using the pseudo-addition law on the Kummer variety.  ... 
arXiv:1709.06063v2 fatcat:itcobgxdofaf7boyzsp4j5h7zq

The overarching finite symmetry group of Kummer surfaces in the Mathieu group M 24

A. Taormina, K. Wendland
2013 Journal of High Energy Physics  
all Kummer surfaces lying on an appropriate path in moduli space connecting the square and the tetrahedral Kummer surfaces.  ...  of lattice embeddings for all Kummer surfaces with Kaehler class induced from the underlying torus.  ...  We also benefitted from conversations with Geoffrey Mason and Michael Tuite, and many participants of the workshop on 'Mathieu Moonshine' at ETH Zurich in July 2011, including its organiser, Matthias Gaberdiel  ... 
doi:10.1007/jhep08(2013)125 fatcat:2yw5edv6ibhwvhbikmgfx22dfq

Computing isogenies between Jacobians of curves of genus 2 and 3

Enea Milio
2019 Mathematics of Computation  
I thank Pierrick Gaudry for suggesting me to work on [10] , for helping me in my first footsteps and for giving me the idea of using the pseudo-addition law on the Kummer variety.  ...  Acknowledgements This research has been done while the author was working as a postdoc in the Caramba team in Nancy.  ...  In genus 3, there is a (64, 28)-configuration for hyperelliptic and non-hyperelliptic curves and for the former, the configuration can be extended to a (64, 29)-configuration. • a = a + a 0 + 2r − θ and  ... 
doi:10.1090/mcom/3486 fatcat:4t6ocsqsgfa67c6b4xy7shkaue

On the Coble quartic [article]

Samuel Grushevsky, Riccardo Salvati Manni
2012 arXiv   pre-print
We review and extend the known constructions relating Kummer threefolds, Gopel systems, theta constants and their derivatives, and the GIT quotient for 7 points in P^2 to obtain an explicit expression  ...  In genus 2, we similarly obtain a short explicit equation for the universal Kummer surface, and relate modular forms of level two to binary invariants of six points on P^1.  ...  All of the computations described above were performed using Maple R , and take a few minutes for a straightforward unoptimized code on a regular PC.  ... 
arXiv:1212.1895v1 fatcat:w2o5rzhcubewvklbecokoe3abm

Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

A.Ya. Bekshaev, S.V. Sviridova
2010 Optics Communications  
General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams.  ...  Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram.  ...  Every practical configuration contains inevitable deviations from the perfect scheme, and knowledge of the role and significance of these deviations is highly desirable for the design and development of  ... 
doi:10.1016/j.optcom.2010.07.031 fatcat:c4p6hn3ayfhz3e6utenrsm4iza

Limits of pluri-tangent planes to quartic surfaces [article]

Ciro Ciliberto, Thomas Dedieu
2014 arXiv   pre-print
., to the union of four general planes, and to a general Kummer surface), the limits as t∈Δ^* tends to 0 of the Severi varieties V_δ(S_t), parametrizing irreducible δ-nodal plane sections of S_t.  ...  We give applications of this to (i) the counting of plane nodal curves through base points in special position, (ii) the irreducibility of Severi varieties of a general quartic surface, and (iii) the monodromy  ...  For example, we obtain Theorem D thinking of the curves in V as cut out by quartic surfaces on a plane embedded in P 3 , and letting this plane degenerate.  ... 
arXiv:1304.7463v3 fatcat:jup46zu4jvfftlfs5vwdromvsq

Hardware-in-the-loop Testbed for Autopilot Development using Flight Simulation and Parallel Kinematics

Stephan Schulz, Hagen Hasberg, Rene Büscher
2020 Zenodo  
This paper presents a testbed for Hardware-in-the-loop stimulation of flight controllers and their sensors in a real-time simulation environment.  ...  Compared to an isolated HIL simulation of a flight controller, this methodology allows simultaneous closed-loop testing of an embedded system with sensors and a flight controller.  ...  ACKNOWLEDGEMENTS The authors would like to acknowledge the financial support of the German Federal Ministry of Economics and Energy (BMWi) for this project under the ZIM program.  ... 
doi:10.5281/zenodo.3757918 fatcat:cta67prcsrckxonx2qaot6dlhm

Study on Magnetic Control Systems of Micro-Robots

Youjia Shao, Ashraf Fahmy, Ming Li, Chunxu Li, Wencang Zhao, Johann Sienz
2021 Frontiers in Neuroscience  
Ultimately, we emphasize the challenges and open problems that urgently need to be settled, and summarize the direction of development in this field, which plays a momentous role in the wide and safe application  ...  For the sake of learning how to apply relevant technologies in medical services, we systematically review pioneering works published in the past and divide magnetic control systems into three categories  ...  A ball screw with a total length of 10 mm is also embedded in the middle of the lower cover, and cooperates with the three ball screws in the upper cover to relatively fix the magnetic ball and prevent  ... 
doi:10.3389/fnins.2021.736730 pmid:34512256 pmcid:PMC8432292 fatcat:p3ocdrwuxfhive3cuppbthkdy4

Numerical Optimization and Map-Based Manipulation With a Quadrupole Electromagnetic Actuated System

Weicheng Ma, Zhijie Huan, Min Xu
2022 Frontiers in Neurorobotics  
This technique shows great potential in the field of precise mechanics, environment protection, and biomedical engineering.  ...  The proposed work provides theoretical references and numerical fundamentals for the control of magnetic particle in future.  ...  magnetic particles in the workspace (Kummer et al., 2010 ).  ... 
doi:10.3389/fnbot.2022.859996 pmid:35370594 pmcid:PMC8967965 fatcat:rqifmitlqrc5takay4bgdzw35q

On tangents to quadric surfaces [article]

Ciprian Borcea, Xavier Goaoc, Sylvain Lazard, Sylvain Petitjean
2004 arXiv   pre-print
We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to configurations of four quadrics admitting a continuum of common tangents.  ...  These considerations are then restricted to spheres in Euclidean three-space, and result in a complete answer to the question over the reals: "When do four spheres allow infinitely many common tangents  ...  It will be observed that the complex case allows more possibilities for degenerate configurations.  ... 
arXiv:math/0402394v1 fatcat:lxuf4acdy5g6viyg5svn542wmy

3D virtual histology of human pancreatic tissue by multiscale phase-contrast X-ray tomography

Jasper Frohn, Diana Pinkert-Leetsch, Jeannine Missbach-Güntner, Marius Reichardt, Markus Osterhoff, Frauke Alves, Tim Salditt
2020 Journal of Synchrotron Radiation  
Cells in such an islet were segmented and visualized in 3D. Further, morphological alterations of tumorous tissue of the pancreas were characterized.  ...  A multiscale three-dimensional (3D) virtual histology approach is presented, based on two configurations of propagation phase-contrast X-ray tomography, which have been implemented in close proximity at  ...  Acknowledgements We thank Michael Sprung and Fabian Westermeier for support during the beam time at P10, Sabine Wolfgramm and Bettina Jeep for excellent technical assistance in performing histology and  ... 
doi:10.1107/s1600577520011327 pmid:33147198 pmcid:PMC7642968 fatcat:lyhhgfodzvga7ea7ejmq4wb6tm

Varieties of Nodal surfaces, coding theory and Discriminants of cubic hypersurfaces. Part 1: Generalities and nodal K3 surfaces. Part 2: Cubic Hypersurfaces, associated discriminants. Part 3: Nodal quintics. Part 4: Nodal sextics [article]

Fabrizio Catanese, Yonghwa Cho, Stephen Coughlan, Davide Frapporti, Alessandro Verra, Michael Kiermaier
2022 arXiv   pre-print
all the 34 possible shortenings of the extended Kummer code K' , and a component is in the closure of another if and only if the code of the latter is a shortening of the code of the former.  ...  nodal surfaces in P^3 of degree d and with n nodes, and their incidence hierarchy, relating partial smoothings to code shortenings.  ...  A slick argument is that we have embedding for the Kummer code K.  ... 
arXiv:2206.05492v2 fatcat:etorsx2kcjgblflezmc347ntze
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