Computational Aspects of Equivariant Hilbert Series of Canonical Rings for Algebraic Curves
, 2022 We study computational aspects of the problem of decomposing finite group actions on graded modules arising in arithmetic geometry, in the context of ordinary representation theory. We provide an algorithm to compute the equivariant Hilbert series of automorphisms acting on canonical rings of projective curves, using the formulas of Chevalley and Weil.
Hara Charalambous +3 more
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Tropical Effective Primary and Dual Nullstellens\"atze [PDF]
, 2015 Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties and algebraic
Grigoriev, Dima, Podolskii, Vladimir V.
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Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces [PDF]
, 2015 This paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. We show that Clarkson's sampling algorithm can be applied to two problems in computational algebra: solving large ...
De Loera, Jesús A. +2 more
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Jacobian Nullwerte, Periods and Symmetric Equations for Hyperelliptic Curves [PDF]
, 2006 We propose a solution to the hyperelliptic Schottky problem, based on the use of Jacobian Nullwerte and symmetric models for hyperelliptic curves.
Guàrdia, J.
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Computing Linear Matrix Representations of Helton-Vinnikov Curves [PDF]
, 2012 Helton and Vinnikov showed that every rigidly convex curve in the real plane bounds a spectrahedron. This leads to the computational problem of explicitly producing a symmetric (positive definite) linear determinantal representation for a given curve. We
A Beauville +18 more
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Point-curve incidences in the complex plane [PDF]
, 2017 We prove an incidence theorem for points and curves in the complex plane. Given a set of $m$ points in ${\mathbb R}^2$ and a set of $n$ curves with $k$ degrees of freedom, Pach and Sharir proved that the number of point-curve incidences is $O\big(m ...
Sheffer, Adam +2 more
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Topological Stability of Kinetic $k$-Centers [PDF]
, 2018 We study the $k$-center problem in a kinetic setting: given a set of continuously moving points $P$ in the plane, determine a set of $k$ (moving) disks that cover $P$ at every time step, such that the disks are as small as possible at any point in time ...
Meulemans, Wouter +4 more
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Analysis of Iterative Methods for the Steady and Unsteady Stokes Problem: Application to Spectral Element Discretizations [PDF]
, 1993 A new and detailed analysis of the basic Uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady Stokes operator is presented.
Maday, Yvon +3 more
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Desingularization in Computational Applications and Experiments [PDF]
, 2013 After briefly recalling some computational aspects of blowing up and of representation of resolution data common to a wide range of desingularization algorithms (in the general case as well as in special cases like surfaces or binomial varieties), we ...
Frühbis-Krüger, Anne
core
Isogenies of Elliptic Curves: A Computational Approach [PDF]
, 2009 Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the reducibility of ...
Shumow, Daniel
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