35 citations · 129 across the 34 of their papers we have counts for
13 papers · 1 filter
G-torsors and universal torsors over nonsplit del Pezzo surfaces
Ulrich Derenthal, Norbert Hoffmann
Let S be a smooth del Pezzo surface that is defined over a field K and splits over a Galois extension L. Let G be either the split reductive group given by the root system of …
Degeneration of torsors over families of del Pezzo surfaces
Ulrich Derenthal, Norbert Hoffmann
Let S be a split family of del Pezzo surfaces over a discrete valuation ring such that the general fiber is smooth and the special fiber has ADE-singularities. Let G be the reducti…
Cox rings of cubic surfaces and Fano threefolds
Ulrich Derenthal, Juergen Hausen, Armand Heim +2
We determine the Cox rings of the minimal resolutions of cubic surfaces with at most rational double points, of blow ups of the projective plane at non-general configurations of si…
Cox rings over nonclosed fields
Ulrich Derenthal, Marta Pieropan
We give a definition of Cox rings and Cox sheaves for varieties over nonclosed fields that is compatible with torsors under quasitori, including universal torsors. We study their e…
Equivariant compactifications of two-dimensional algebraic groups
Ulrich Derenthal, Daniel Loughran
We classify generically transitive actions of semidirect products of an additive and a multiplicative group on the projective plane. Motivated by the program to study the distribut…
On the factor alpha in Peyre's constant
Ulrich Derenthal, Andreas-Stephan Elsenhans, Jörg Jahnel
For an arbitrary del Pezzo surface S, we compute alpha(S), which is the volume of a certain polytope in the dual of the effective cone of S, using Magma and Polymake. The constant…