Toric manifolds with degenerate dual variety and defect polytopes

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We classify projective toric manifolds whose dual variety is not a hypersurface in the dual projective space. Under the standard dictionary between toric geometry and convex geometry, they correspond to certain convex Delzant integer polytopes, P, which we call defect polytopes. Using the geometrical classification we give a detailed description of defect polytopes and prove that they are characterized by the vanishing of a combinatorial invariant, denoted by c(P). We further prove that a related invariant, c*(P), is nonnegative, for any simple convex integral polytope.
14 pages, 2 figures. Reference [GKZ] added. A new invariant is introduced. The statement 3.4 is proved for simple polytopes

Keywords

Algebraic Geometry, Combinatorics, 14M25, 52B20, 05A18

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/67424

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0305150
 http://arxiv.org/abs/math/0305150

Collections

arXiv