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Homogeneous coordinates and quotient presentations for toric varieties (2000)
| Venue: | MATH. NACHR |
| Citations: | 10 - 3 self |
BibTeX
@ARTICLE{A'Campo-Neuen00homogeneouscoordinates,
author = {Annette A'Campo-Neuen and Jürgen Hausen and Stefan Schröer},
title = {Homogeneous coordinates and quotient presentations for toric varieties},
journal = {MATH. NACHR},
year = {2000},
pages = {5--19}
}
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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 Q-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.
Keyphrases
toric variety homogeneous coordinate quotient presentation quasicoherent sheaf quasiaffine toric variety projective toric variety free quotient geometric quotient arbitrary toric variety quotient presentation yield homogeneous coordinate cartier divisor q-cartier divisor quotient presentation correspond weil divisor
