Lattice points in Minkowski sums

Abstract

Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact that does not need the smoothness assumption on P.

5 pages, 4 figures

Cited by in corpus (8)

• Product-Mix Auctions and Tropical Geometry
• Positivity for toric vector bundles
• Projective normality of nonsingular toric varieties of dimension three
• Cayley sums and Minkowski sums of lattice polytopes
• Intrinsicness of the Newton polygon for smooth curves on ${\mathbb{P}}^1\times {\mathbb{P}}^1$
• Integer decomposition property of polytopes
• Nef and big divisors on toric weak Fano 3-folds
• Unimodular covers of 3-dimensional parallelepipeds and Cayley sums