Agnieszka Bodzenta

Title: Tilting relative generators for birational morphisms

Abstract:
For a birational morphism of smooth varieties f: X \to Y with the 
dimension of fibers bounded by one, the derived category of X admits 
a relative tilting object over Y. It is a direct sum of copies of the 
canonical line bundle restricted to relative canonical divisors of 
partial contractions g: X \to Z. It endows the derived category of X 
with a t-structure related to the map f. I will show that Y is the 
fine moduli space of simple quotients of O_X in the heart of this 
t-structure. I will also prove that the t-structures for f and any 
partial contraction g are related by two tilts in torsion pairs. 
This is a joint work with A. Bondal.