## Department of Mathematics

Algebra and Geometry Seminar

# Agnieszka Bodzenta (University of Warsaw)

Hjoernet, Realfagbygget 4. et.

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.