# Torus invariant divisors

@article{Petersen2011TorusID,
title={Torus invariant divisors},
author={Lars Petersen and Hendrik S{\"u}{\ss}},
journal={Israel Journal of Mathematics},
year={2011},
volume={182},
pages={481-504}
}
• Published 4 November 2008
• Mathematics
• Israel Journal of Mathematics
Using the language of Altmann, Hausen and Süß, 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…

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## References

SHOWING 1-10 OF 13 REFERENCES

### Gluing Affine Torus Actions Via Divisorial Fans

• Mathematics
• 2006
Generalizing the passage from a fan to a toric variety, we provide a combinatorial approach to construct arbitrary effective torus actions on normal, algebraic varieties. Based on the notion of a

### Cartier divisors and geometry of normalG-varieties

We study Cartier divisors on normal varieties with the action of a reductive groupG. We give criteria for a divisor to be Cartier, globally generated and ample, and apply them to a study of the local

### Polyhedral Divisors and Algebraic Torus Actions

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 approach

### Normal affine surfaces with C*-actions

• Mathematics
• 2003
A classification of normal affine surfaces admitting a $\bf C^*$-action was given in the work of Bia{\l}ynicki-Birula, Fieseler and L. Kaup, Orlik and Wagreich, Rynes and others. We provide a simple

### Classification of G-varieties of complexity?1

We consider the problem of finding a combinatorial description of the algebraic varieties in a given birational class that admit an action of a reductive group G. This is a direct generalization of

### ALGEBRAIC SURFACES WITH k*-ACTION

• Mathematics
• 2006
Let k be an arbitrary algebraically closed field and let k* denote the multiplicative group of k considered as an algebraic group. We give a complete classification of all non-singular projective

### Affine $\mathbb{T}$-varieties of complexity one and locally nilpotent derivations

Let X = Spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus $\mathbb{T}$ of dimension n. Let also ∂ be a

### Multiplier ideal sheaves and analytic methods in algebraic geometry

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Preliminary Material . . . . . . . . . . . . . . .