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Homogeneous Coordinates for Algebraic Varieties (2002)
| Content Provider | CiteSeerX |
|---|---|
| Author | Berchtold, Florian Hausen, Jürgen |
| Abstract | 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. |
| File Format | |
| Publisher Date | 2002-01-01 |
| Access Restriction | Open |
| Subject Keyword | Homogeneous Coordinate Normal Complex Variety Homogeneous Coordinate Ring Constant Invertible Global Function Usual Homogeneous Coordinate Ring Constant Global Function Factorial Complete Irreducible Variety Projective Space Unique Factorization Divisorial Toric Variety Algebraic Variety Faithful Functor Homogeneous Coordinate Ring Defines Picard Group Generated Picard Group Krull Ring |
| Content Type | Text |
