Homogeneous Coordinates and Quotient Presentations for Toric Varieties
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 $\QQ$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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2000
 arXiv:
 arXiv:math/0005083
 Bibcode:
 2000math......5083A
 Keywords:

 Algebraic Geometry;
 14M25;
 14C20;
 14L30;
 14L32
 EPrint:
 minor changes, to appear in Math. Nachr., 13 pages, 2 figures