Tuesday, April 8, 14:00, 7.527

Agnieszka Bodzenta-Skibinska (Warsaw)
Derived categories of coherent sheaves, I and II.

Abstract:
I will talk on bounded derived categories of coherent sheaves in the study of algebraic varieties. I will recall the most important results and conjectures of the last few years. Then I will focus on the situation when a smooth variety $X$ admits a full exceptional collection. I will define a DG quiver which describes the bounded derived category in this case. In the second part of my talk I will discuss methods of calculating the DG quiver. I will explain how highest weight categories appear in the picture. Finally, I will use the corresponding quasi-hereditary algebras to relate the derived category to the canonical divisor of a variety.