2022/03/09 by Benjamin Nill, Nill, Benjamin
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2203.04620
openalex publication_date 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A d-dimensional lattice polytope P is Gorenstein if it has a multiple r P that is a reflexive polytope up to translation by a lattice vector. The difference d+1-r is called the degree of P. We show that a Gorenstein polytope is a lattice pyramid if its dimension is at least three times its degree. This was previously conjectured by Batyrev and Juny. We also present a refined conjecture and prove it for IDP Gorenstein polytopes.