Polyhedral Divisors and Algebraic Torus Actions

Details Polyhedral Divisors and Algebraic Torus Actions Polyhedral Divisors and Algebraic Torus Actions

2003-06-19

arxiv.org/abs/math/0306285v2

Math. Ann. 334, 557-607 (2006)

Mathematics

Algebraic Geometry

Major revision, new results added, to appear in Math. Ann., 40 pages

Scientific paper

We provide a complete description of normal affine varieties with effective
algebraic torus action in terms of what we call proper polyhedral divisors on
semiprojective varieties. Our theory extends classical cone constructions of
Dolgachev, Demazure and Pinkham to the multigraded case, and it comprises the
theory of affine toric varieties.

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