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Homogeneous Coordinates and Quotient Presentations for Toric Varieties
Author(s) -
A'Campo–Neuen Annette,
Hausen Jürgen,
Schröer Stefan
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200212)246:1<5::aid-mana5>3.0.co;2-c
Subject(s) - mathematics , quotient , toric variety , morphism , pure mathematics , homogeneous , homogeneous coordinates , algebra over a field , combinatorics
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.