Stratification of Projection Maps From Toric Varieties
Boulos El Hilany, Martin Helmer, and Elias Tsigaridas

TL;DR
This paper introduces a combinatorial approach to stratify projection maps from toric varieties, providing an algorithm that outperforms existing methods in computing Whitney stratifications.
Contribution
It develops a constructive combinatorial version of Thom's Isotopy Lemma tailored for toric varieties, linking Whitney strata to polytope faces.
Findings
Algorithm outperforms existing methods in examples
Provides a constructive, combinatorial stratification method
Applicable to both complex and real toric varieties
Abstract
We prove a combinatorial version of Thom's Isotopy Lemma for projection maps applied to any complex or real toric variety. Our results are constructive and give rise to a method for associating the Whitney strata of the projection to the faces of the polytope of the corresponding toric variety. For all examples we produced, our resulting algorithm outperforms known general purpose methods in Helmer and Nanda (FoCM, 2022), and Dinh and Jelonek (DCG, 2021) for computing map-stratifications.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Artificial Intelligence in Games
