Ulrich Derenthal, University of Goettingen
Universal torsors and Cox rings of singular cubic surfaces

Universal torsors were introduced by Colliot-Thélène and Sansuc in order to study the Hasse principle on Del Pezzo surfaces. Later, they were applied successfully to other problems in arithmetic geometry.

The easiest example is the n-dimensional affine space with the origin removed, which is the universal torsor over the (n-1)-dimensional projective space.

In 2004, Hassett and Tschinkel developed a new method of constructing universal torsors of cubic surfaces as subsets of the variety associated to the total coordinate ring (Cox ring). I will introduce these concepts, especially by constructing the Cox ring of a certain singular cubic surface.