The topic of the talk is the study of syzygies of graded rings, more precisely homogeneous coordinate rings of algebraic varieties. These are special graded rings where the structure of the syzygy modules can be understood to some extent using a mixture of algebraic and geometric methods. The guiding question is how to guarantee that the first few syzygy modules will be as simple as possible, a line of research started in the case at hand by Green and Lazarsfeld thirty years ago. The concrete class of varieties we look at are complete group varieties, the methods will range from vanishing theorems to convex geometry (in the form of Newton-Okounkov bodies). If time permits we will mention results of similar flavour for moduli spaces of sheaves. This is an account of joint work with Victor Lozovanu und Yusuf Mustopa.


Speaker(s): Alex Kuronya (Goethe-Universität Frankfurt)