This thesis is concerned with the Hodge-theoretic relation between polarized K3 surfaces of degree d and special cubic fourfolds of discriminant d, as introduced by Hassett.
For half of the d, K3 surfaces associated ......

This thesis consists of four parts which investigate different aspects of Hodge classes on self-products of K3 surfaces.
In the first three parts we present three different strategies to tackle the Hodge conjecture ...

The formal Hermitean 1-matrix model is shown to be equivalent to an effective field theory. The correlation functions and the free energy of the matrix model correspond directly to the correlation functions and the free ...

In this thesis, we study a new class of triangulated categories associated with singularities of algebraic varieties. For Gorenstein rings, triangulated singularity categories were introduced by Buchweitz. In 2006 Orlov ...

Let F be a finite extension over the field of 2-adic numbers. In this paper, we construct a Rapoport-Zink-space for the split unitary group in two variables over a ramified quadratic extension of F. For this, we first ...