Akihiro Higashitani: Regular unimodular triangulations of dilated empty simplices and Gröbner basis

Abstract

We say that a simplex is empty if it is a lattice simplex which contains no lattice points except for its vertices. Empty simplices play a crucial role in combinatorics of lattice polytopes. On the other hand, the existence of a (regular) unimodular triangulation of a lattice polytope is of quite importance in several points of view. In this talk, we will discuss the existence of a regular unimodular triangulation of a dilation of certain empty simplices. Our proof is given by using the technique of Gröbner basis of the toric ideal associated to a lattice polytope. This talk is based on the joint work with Takayuki Hibi and Koutarou Yoshida (Osaka University).