• Corpus ID: 9124434

Canonical divisors on T-varieties

  title={Canonical divisors on T-varieties},
  author={Hendrik Suss},
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… 

Figures from this paper

Deformations of rational T-varieties

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

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

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

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

The Cox ring of an algebraic variety with torus action

Deformations of smooth toric surfaces

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



Gluing Affine Torus Actions Via Divisorial Fans

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

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

The versal deformation of an isolated toric Gorenstein singularity

Given a lattice polytope Q ⊆ ℝn, we define an affine scheme that reflects the possibilities of splitting Q into a Minkowski sum. Denoting by Y the toric Gorenstein singularity induced by Q, we

Normal affine surfaces with C*-actions

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 Toric log Del Pezzo Surfaces having Picard Number 1 and Index ≤ 3

Abstract.Toric log Del Pezzo surfaces with Picard number 1 have been completely classified whenever their index is ≤ 2. In this paper we extend the classification for those having index 3. We prove

Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV1,...,Vr in a toric

On Gorenstein log del Pezzo Surfaces

In this paper, we first present the complete list of the singularity types of the Picard number one Gorenstein log del Pezzo surface and the number of the isomorphism classes with the given

Completions of $\C^*$-surfaces

Following an approach of Dolgachev, Pinkham and Demazure, we classified in math.AG/0210153 normal affine surfaces with hyperbolic C^{*}-actions in terms of pairs of Q-divisors (D+,D-) on a smooth

Gorenstein log del Pezzo Surfaces of Rank One

Fano 3-FOLDS. I

This article contains a classification of special Fano varieties; we give a description of the projective models of Fano 3-folds of index r ≥ 2 and of hyperelliptic Fano 3-folds.Bibliography: 31