A simple combinatorial criterion for projective toric manifolds with dual defect

Autores: Alicia Dickenstein, Benjamin Nill
Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 2-3, 2010, págs. 435-448
Idioma: inglés
DOI: 10.4310/mrl.2010.v17.n3.a5
Enlaces
- Texto completo (pdf)
Resumen
- We show that any smooth lattice polytope $P$ with codegree greater or equal than $(\dim(P)+3)/{2}$ (or equivalently, with degree smaller than ${\dim (P)}/{2}$), defines a dual defective projective toric manifold. This implies that $P$ is $\Q$-normal (in the terminology of \cite{DDP09}) and answers partially an adjunction-theoretic conjecture by Beltrametti-Sommese (see \cite{BSW92},\cite{BS95},\cite{DDP09}). Also, it follows from \cite{DR06} that smooth lattice polytopes with this property are precisely strict Cayley polytopes, which completes the answer in \cite{DDP09} of a question in \cite{BN07} for smooth polytopes.