Homogeneous coordinates for algebraic varieties

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We associate to every divisorial (e.g. smooth) variety $X$ with only constant invertible global functions and finitely generated Picard group a $Pic(X)$-graded homogeneous coordinate ring. This generalizes the usual homogeneous coordinate ring of the projective space and constructions of Cox and Kajiwara for smooth and divisorial toric varieties. We show that the homogeneous coordinate ring defines in fact a fully faithful functor. For normal complex varieties $X$ with only constant global functions, we even obtain an equivalence of categories. Finally, the homogeneous coordinate ring of a locally factorial complete irreducible variety with free finitely generated Picard group turns out to be a Krull ring admitting unique factorization.
30 pages

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Algebraic Geometry, 13A02, 13A50, 14C20, 14C22

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http://salesiana.dossiersoluciones.com/handle/123456789/65800

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0211413
 http://arxiv.org/abs/math/0211413
 J. Algebra 266, 636-670 (2003)

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arXiv