Cayley decompositions of lattice polytopes and upper bounds for h*-polynomials
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Abstract
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.
Polytopes with nontrivial Cayley decompositions correspond to projectivized sums of toric line bundles, and our approach is partially inspired by classification results of Fujita and others in algebraic geometry. In an appendix, we interpret our Cayley decomposition theorem in terms of adjunction theory for toric varieties.
© Walter de Gruyter Berlin · New York 2009
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- On Hartogs' extension theorem on (n – 1)-complete complex spaces
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- A short proof of the λg-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves
- Unobstructedness of deformations of holomorphic maps onto Fano manifolds of Picard number 1
- Cayley decompositions of lattice polytopes and upper bounds for h*-polynomials
- Siegel's trace problem and character values of finite groups
Articles in the same Issue
- Trees and mapping class groups
- The Hartogs extension theorem on (n – 1)-complete complex spaces
- On Hartogs' extension theorem on (n – 1)-complete complex spaces
- Cohomological finiteness conditions for elementary amenable groups
- The behaviour of the differential Galois group on the generic and special fibres: A Tannakian approach
- Discrete holomorphic geometry I. Darboux transformations and spectral curves
- Multilinear morphisms between 1-motives
- A short proof of the λg-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves
- Unobstructedness of deformations of holomorphic maps onto Fano manifolds of Picard number 1
- Cayley decompositions of lattice polytopes and upper bounds for h*-polynomials
- Siegel's trace problem and character values of finite groups
