Cayley decompositions of lattice polytopes and upper bounds for h^*-polynomials

Details Cayley decompositions of lattice polytopes and upper bounds for h^*-polynomials Cayley decompositions of lattice polytopes and upper bounds for h^*-polynomials

2008-04-23

arxiv.org/abs/0804.3667v1

J. Reine Angew. Math. 637 (2009), 207-216

Mathematics

Combinatorics

AMS-LaTeX, 9 pages

Scientific paper

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.

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