An irreducible algebraic variety X is rigid if it admits no nontrivial action of the additive group
of the ground field. We prove that the automorphism group of a rigid affine variety contains a …

We consider rational varieties with a torus action of complexity one and extend the
combinatorial approach via the Cox ring developed for the complete case in earlier work to …

Following the work of Altmann and Hausen we give a combinatorial description for smooth
Fano threefolds admitting a 2-torus action. We show that a whole variety of properties and …

On rigidity of factorial trinomial hypersurfaces Page 1 International Journal of Algebra and
Computation Vol. 26, No. 5 (2016) 1061–1070 c© World Scientific Publishing Company DOI …

We classify generically transitive actions of semi-direct products on ℙ2. Motivated by the
program to study the distribution of rational points on del Pezzo surfaces (Manin's …

This thesis contributes to the explicit classification of Fano varieties of Picard number one
and two. In the first chapter we give sharp upper bounds on various geometric invariants of …

We present an algorithm to compute the automorphism group of a Mori dream space. As an
example calculation, we determine the automorphism groups of singular cubic surfaces with …

Given a connected reductive algebraic group G and a Borel subgroup B⊆ G, we study B-
normalized one-parameter additive group actions on affine spherical G-varieties. We …

We consider log del Pezzo surfaces coming with a non-trivial torus action. Such a surface is
1/k-log canonical if it allows a resolution of singularities with discrepanies all greater or …

The subject of this thesis are varieties with a torus action of complexity one, ie algebraic
varieties X with an algebraic torus T acting effectively on them, where dim (T)= dim (X)-1. A …