Defect Polytopes and Counter-Examples With polymake
Michael Joswig, Andreas Paffenholz
TL;DR
This paper demonstrates the use of polymake software to compute and analyze defect polytopes and A-determinants, providing counter-examples to existing conjectures in toric geometry.
Contribution
It introduces a method for using polymake to construct counter-examples in toric geometry, advancing computational approaches in the field.
Findings
Counter-examples to conjectures on A-determinants
Counter-examples to defect polytopes
Validation of computational methods in toric geometry
Abstract
It is demonstrated how the software system polymake can be used for computations in toric geometry. More precisely, counter-examples to conjectures related to A-determinants and defect polytopes are constructed.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Geometric and Algebraic Topology