English

Homogeneous Coordinates and Quotient Presentations for Toric Varieties

Algebraic Geometry 2007-05-23 v2

Abstract

Generalizing cones over projective toric varieties, we present arbitrary toric varieties as quotients of quasiaffine toric varieties. Such quotient presentations correspond to groups of Weil divisors generating the topology. Groups comprising Cartier divisors define free quotients, whereas \QQ\QQ-Cartier divisors define geometric quotients. Each quotient presentation yields homogeneous coordinates. Using homogeneous coordinates, we express quasicoherent sheaves in terms of multigraded modules and describe the set of morphisms into a toric variety.

Keywords

Cite

@article{arxiv.math/0005083,
  title  = {Homogeneous Coordinates and Quotient Presentations for Toric Varieties},
  author = {A. A'Campo-Neuen and J. Hausen and S. Schroeer},
  journal= {arXiv preprint arXiv:math/0005083},
  year   = {2007}
}

Comments

minor changes, to appear in Math. Nachr., 13 pages, 2 figures