We show that the following classes of lattice polytopes have unimodular covers, in
dimension three: the class of parallelepipeds, the class of centrally symmetric polytopes, and …

We study the integer decomposition property of lattice polytopes associated with the $ n $-
dimensional smooth complete fans with at most $ n+ 3$ rays. Using the classification of …

In this paper, we discuss the toric ideals of the Minkowski sums of unit simplices. More
precisely, we prove that the toric ideal of the Minkowski sum of unit simplices has a …

We show that:(1) unimodular simplices in a lattice 3-polytope cover a neighborhood of the
boundary of the polytope if and only if the polytope is very ample,(2) the convex hull of lattice …

These are notes of a five-talk lecture during the “Summer Workshop on Lattice Polytopes”, at
Osaka University on July 23rd–August 10th, 2018. Toric varieties are algebraic varieties …

Scope. A lattice polytope in Rd is the convex hull of a finite number of points in the lattice Zd.
Recently, Chervet, Grappe, and Robert [5] introduced a class of lattice polytopes with strong …

Diese Disseration beschäftigt sich mit dem Zusammenspiel von Polytopen und Gittern. Die
Motivation für die Untersuchung von Gitterpolytopen kommt dabei aus zwei sehr …

Algebraic and Geometric Combinatorics on Lattice Polytopes : Some lattice parallelepipeds
with unimodular covers Page 1 85 Some lattice parallelepipeds with unimodular covers …

Algebraic and Geometric Combinatorics on Lattice Polytopes : Open problems from the 2018
Summer Workshop on Lattice Polytopes at Page 1 450 Open problems from the 2018 Summer …