2017/11/27 by Hofscheier, Johannes, Katthän, Lukas, Nill, Benjamin
#05E40 #14H45 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 52B20 #Secondary: 13A02
paper · doi:10.48550/arxiv.1711.09512
A lattice polytope P is called IDP if any lattice point in its kth dilate is a sum of k lattice points in P. In 1991 Stanley proved a strong inequality in Ehrhart theory for IDP lattice polytopes. We show that his conclusion holds under much milder assumptions, namely if the lattice polytope P is spanning, i.e., any lattice point of the ambient lattice is an integer affine combination of lattice points in P. As an application, we get a generalization of Hibi's Lower Bound Theorem. Our proof relies on generalizing Bertini's theorem to the semistandard situation and Harris' Uniform Position Principle to certain curves in weighted projective space.