From Hodge theory for tame functions to Ehrhart theory for polytopes
Antoine Douai
TL;DR
This paper explores the connection between Hodge theory for tame functions and Ehrhart theory for polytopes, analyzing the Poincaré polynomial of the Hodge filtration to reveal new insights.
Contribution
It introduces a novel link between mixed Hodge structures for regular functions and Ehrhart theory, expanding understanding of their interplay.
Findings
Analysis of the Poincaré polynomial reveals new structural properties.
Establishment of a theoretical connection between Hodge structures and polytope counting.
Potential applications to algebraic geometry and combinatorics.
Abstract
We study the interplay between Sabbah's mixed Hodge structure for regular functions and Ehrhart theory for polytopes. To this end, we analyze the properties of the Poincar\'e polynomial of the Hodge filtration of this mixed Hodge structure.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications