# Canonical divisors on T-varieties

@inproceedings{Suss2008CanonicalDO, title={Canonical divisors on T-varieties}, author={Hendrik Suss}, year={2008} }

Generalising toric geometry we study compact varieties admitting lower dimensional torus actions. In particular we describe divisors on them in terms of convex geometry and give a criterion for their ampleness. These results may be used to study Fano varieties with small torus actions. As a first result we classify log del Pezzo C∗-surfaces of Picard number 1 and Gorenstein index ≤ 3. In further examples we show how classification might work in higher dimensions and we give explicit…

## 8 Citations

### Deformations of rational T-varieties

- Mathematics
- 2012

We show how to construct certain homogeneous deformations for rational normal varieties with codimension one torus action. This can then be used to construct homogeneous deformations of any toric…

### Rational singularities of normal T-varieties

- Mathematics
- 2009

A T-variety is an algebraic variety X with an effective regular action of an algebraic torus T. Altmann and Hausen gave a combinatorial description of an affine T-variety X by means of polyhedral…

### Okounkov Bodies of Complexity-One T-Varieties

- Mathematics
- 2011

We compute Okounkov bodies of projective complexity-one T-varieties with respect to two types of invariant flags. In particular, we show that the latter are rational polytopes. Moreover, using…

### Deformations of rational varieties with codimension-one torus action

- Mathematics
- 2010

Eidesstattliche Erklarung Abstract Table of Contents List of Figures Remarks
on Notation Introduction T-Varieties Preliminaries on Deformations Homogeneous
Deformations of Nonaffine T-Varieties…

### Deformations of smooth toric surfaces

- Mathematics
- 2011

For a complete, smooth toric variety Y, we describe the graded vector space $${T_Y^1}$$. Furthermore, we show that smooth toric surfaces are unobstructed and that a smooth toric surface is rigid if…

### A G ] 3 0 O ct 2 00 9 Polarized Complexity-One T-Varieties

- 2009

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