Gorenstein simplices and the associated finite abelian groups

Abstract

It is known that a lattice simplex of dimension $d$ corresponds a finite abelian subgroup of $(\mathbb{R}/\mathbb{Z}{)}^{d+1}$. Conversely, given a finite abelian subgroup of $(\mathbb{R}/\mathbb{Z}{)}^{d+1}$ such that the sum of all entries of each element is an integer, we can obtain a lattice simplex of dimension $d$. In this paper, we discuss a characterization of Gorenstein simplices in terms of the associated finite abelian groups. In particular, we present complete characterizations of Gorenstein simplices whose normalized volume equals $p,p^2$ and $pq$, where $p$ and $q$ are prime numbers with $p\ne q$. Moreover, we compute the volume of the dual simplices of Gorenstein simplices.

18 pages, to appear in European Journal of Combinatorics

References in corpus (2)

• Lattice polytopes having h^*-polynomials with given degree and linear coefficient
• Gorenstein polytopes with trinomial $h^{\ast }$-polynomials

Cited by in corpus (1)

• Gorenstein simplices with a given $\delta$-polynomial