Akiyoshi Tsuchiya: The reflexive dimension of a (0,1)-polytope

Abstract

A reflexive polytope is one of the keywords belonging to the current trends on the research of lattice polytopes. In fact, many authors have studied reflexive polytopes from viewpoints of combinatorics, commutative algebra and algebraic geometry. It is known that every lattice polytope is unimodularly equivalent to a face of some reflexive polytope. A stronger question is to ask whether every (0,1)-polytope is unimodularly equivalent to a facet of some reflexive polytope. In this talk, we show that for several classes of (0,1)-polytopes, this question is true. In particular, we consider a large class of (0,1)-polytopes, the edge polytopes of finite simple graphs. This talk is based on joint work with Takahiro Nagaoka.