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arXiv · 2404.03975

Thin Simplices via Modular Arithmetic

Vadym Kurylenko
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Abstract

The local $h^*$-polynomial is a natural invariant of a lattice polytope appearing in Ehrhart theory and Hodge theory. In this work, we study the question posed in [GKZ94] concerning the classification of lattice simplices with vanishing local $h^*$-polynomial. Such simplices are called thin. We relate this question to linear codes and hyperplane arrangements over finite rings. This allows us to obtain a complete classification of the $4$-dimensional thin simplices, extending the previously known results in dimensions up to $3$.

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Vadym Kurylenko. 2025-12-22. Thin Simplices via Modular Arithmetic. https://arxiv.org/abs/2404.03975

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