Homogeneous coordinates for algebraic varieties : Revised Version

Berchtold, Florian; Hausen, Jürgen

Homogeneous coordinates for algebraic varieties : Revised Version

Files

preprint_161_02.pdf(320.47 KB)

Date

2002

Authors

Berchtold, Florian

Hausen, Jürgen

Series

Konstanzer Schriften in Mathematik und Informatik; 161

Publication type

Preprint

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.

Subject (DDC)

004 Computer Science

Cite This

ISO 690

BERCHTOLD, Florian, Jürgen HAUSEN, 2002. Homogeneous coordinates for algebraic varieties : Revised Version

BibTex

@unpublished{Berchtold2002Homog-6147,
  year={2002},
  title={Homogeneous coordinates for algebraic varieties : Revised Version},
  author={Berchtold, Florian and Hausen, Jürgen}
}

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