A Simple Combinatorial Criterion for Projective Toric Manifolds with Dual Defect

A. DICKENSTEIN, B. NILL

MATHEMATICAL RESEARCH LETTERS

INT PRESS BOSTON, INC

Año: 2010 vol. 17 p. 435 - 448

1073-2780

Abstract. We show that any smooth lattice polytope P with codegree greater or equalthan (dim(P) + 3)/2 (or equivalently, with degree smaller than dim(P)/2), defines adual defective projective toric manifold. This implies that P is Q-normal (in the terminologyof [Dickenstein-di Rocco-Piene]) and answers partially an adjunction-theoretic conjecture by Beltrametti- Sommese. Also, it follows from [di Rocco] that smooth lattice polytopes withthis property are precisely strict Cayley polytopes, which completes the answer in [Dickenstein-di Rocco-Piene] of a question in [Batyrev-Nill] for smooth polytopes.