%0 Journal Article
%T Cayley decompositions of lattice polytopes and upper bounds for h^*-polynomials
%A Christian Haase
%A Benjamin Nill
%A Sam Payne
%J Mathematics
%D 2008
%I arXiv
%X We give an effective upper bound on the h^*-polynomial of a lattice polytope in terms of its degree and leading coefficient, confirming a conjecture of Batyrev. We deduce this bound as a consequence of a strong Cayley decomposition theorem which says, roughly speaking, that any lattice polytope with a large multiple that has no interior lattice points has a nontrivial decomposition as a Cayley sum of polytopes of smaller dimension. In an appendix, we interpret this result in terms of adjunction theory for toric varieties.
%U http://arxiv.org/abs/0804.3667v1