Crepant Resolutions of Gorenstein Toric Singularities and Upper Bound Theorem

TL;DR

This paper explores conditions for crepant resolutions of Gorenstein toric singularities using a variant of the Upper Bound Theorem applicable to simplicial balls, providing insights into toric geometry.

Contribution

It introduces a necessary condition for torus-equivariant crepant resolutions based on a modified Upper Bound Theorem for simplicial balls.

Findings

Derived a necessary condition for crepant resolutions

Linked toric singularities to combinatorial topology

Utilized a variant of the Upper Bound Theorem

Abstract

A necessary condition for the existence of torus-equivariant crepant resolutions of Gorenstein toric singularities can be derived by making use of a variant of the classical Upper Bound Theorem which is valid for simplicial balls.