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

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Haase, Christian
Nill, Benjamin
Payne, Sam
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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.
Comment: AMS-LaTeX, 9 pages
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Mathematics - Combinatorics, Mathematics - Algebraic Geometry, 52B20 (Primary), 14M25, 14C20 (Secondary)
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