Wronski Pairs of Honeycomb Curves
Laura Casabella, Michael Joswig, Rafael Mohr

TL;DR
This paper investigates Wronski pairs of honeycomb curves, exploring their real solutions and computational challenges using algebraic geometry algorithms, advancing understanding of polynomial systems related to convex polytope triangulations.
Contribution
It introduces a detailed study of Wronski pairs of honeycomb curves, linking algebraic geometry with computational methods to analyze real solutions of polynomial systems.
Findings
Analysis of real solutions in Wronski systems
Development of computational approaches using Gr"obner bases
Insights into algebraic and numerical methods for polynomial systems
Abstract
We study certain generic systems of real polynomial equations associated with triangulations of convex polytopes and investigate their number of real solutions. Our main focus is set on pairs of plane algebraic curves which form a so-called Wronski system. The computational tasks arising in the analysis of such Wronski pairs lead us to the frontiers of current computer algebra algorithms and their implementations, both via Gr\"obner bases and numerical algebraic geometry.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory
