Torus invariant divisors

Details Torus invariant divisors Torus invariant divisors

2008-11-04

arxiv.org/abs/0811.0517v3

Israel Journal of Mathematics Volume 182 (2011), No. 1, 481-504

Mathematics

Algebraic Geometry

16 pages; 5 pictures; small changes in the layout, further typos removed

Scientific paper

10.1007/s11856-011-0039-z

Using the language of polyhedral divisors and divisorial fans we describe invariant divisors on normal varieties X which admit an effective codimension one torus action. In this picture X is given by a divisorial fan on a smooth projective curve Y. Cartier divisors on X can be described by piecewise affine functions h on the divisorial fan S whereas Weil divisors correspond to certain zero and one dimensional faces of it. Furthermore we provide descriptions of the divisor class group and the canonical divisor. Global sections of line bundles O(D_h) will be determined by a subset of a weight polytope associated to h, and global sections of specific line bundles on the underlying curve Y.

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