Abstract
AbstractA d-dimensional lattice polytope P is Gorenstein if it has a multiple rP that is a reflexive polytope up to translation by a lattice vector. The difference $$d+1-r$$
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.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Theoretical Computer Science
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