Hendrik Süß

THE GEOMETRY OF T-VARIETIES

This survey paper is based on my IMPANGA lectures given in the Banach Center, Warsaw in January 2011. We study the moduli of holomorphic map germs from the complex line into complex compact manifolds with applications in global singularity theory and the theory of hyperbolic algebraic varieties.We give a light introduction to some recent developments in Mori theory, and to our recent direct proof of the finite generation of the canonical ring.We introduce a variety

Polarized complexity-1 T-varieties

\hat{G}_2

K-Stability for Fano Manifolds with Torus Action of Complexity 1

parameterizing isotropic five-spaces of a general degenerate four-form in a seven dimensional vector space. It is in a natural way a degeneration of the variety

Kähler-Einstein metrics on symmetric Fano T-varieties

G_2

On the classification of Kähler–Ricci solitons on Gorenstein del Pezzo surfaces

, the adjoint variety of the simple Lie group

Flexible affine cones and flexible coverings

\mathbb{G}_2

The Cox ring of an algebraic variety with torus action

. It occurs that it is also the image of

Canonical divisors on T-varieties

\mathbb{P}^5

Fano threefolds with 2-torus action - a picture book

by a system of quadrics containing a twisted cubic. Degenerations of this twisted cubic to three lines give rise to degenerations of

Multigraded Factorial Rings and Fano Varieties with Torus Action

G_2