Bunches of cones in the divisor class group -- A new combinatorial language for toric varieties

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

As an alternative to the description of a toric variety by a fan in the lattice of one parameter subgroups, we present a new language in terms of what we call bunches -- these are certain collections of cones in the vector space of rational divisor classes. The correspondence between these bunches and fans is based on classical Gale duality. The new combinatorial language allows a much more natural description of geometric phenomena around divisors of toric varieties than the usual method by fans does. For example, the numerically effective cone and the ample cone of a toric variety can be read off immediately from its bunch. Moreover, the language of bunches appears to be useful for classification problems.
Minor changes, to appear in Int. Math. Res. Not

Keywords

Algebraic Geometry, 14M25; 14C20; 52B35

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/66983

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304055
 http://arxiv.org/abs/math/0304055
 Int. Math. Res. Not. 2004, No. 6, 261-302 (2004)

Collections

arXiv