Tuesday, April 8, 14:00, 7.527
Agnieszka Bodzenta-Skibinska (Warsaw)
Derived categories of coherent sheaves, I and II.
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
algebras to relate the derived category to the canonical divisor of a variety.