Homogeneous Coordinates and Quotient Presentations for Toric Varieties

Details Homogeneous Coordinates and Quotient Presentations for Toric Varieties Homogeneous Coordinates and Quotient Presentations for Toric Varieties

2000-05-09

arxiv.org/abs/math/0005083v2

Math. Nachr. 246-247, 5-19 (2002)

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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