Abstract / Description of output
Using the language of Altmann, Hausen and Su, 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.
Original language | English |
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Pages (from-to) | 481-504 |
Number of pages | 24 |
Journal | Israel journal of mathematics |
Volume | 182 |
Issue number | 1 |
DOIs | |
Publication status | Published - Mar 2011 |
Keywords / Materials (for Non-textual outputs)
- GEOMETRY
- VARIETIES
- SURFACES