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A. Bondal Seminar
February 17, 2005, Moscow, Steklov Mathematical Institute, Room 540 (8 Gubkina)

Joint meeting with the seminar "Geometry of Algebraic Varieties"

T-structures on some local Calabi–Yau varieties (after T. Bridgeland)

A. G. Kuznetsov

Abstract: Let $Z$ be a Fano variety satisfying the condition that the rank of the Grothendieck group of $Z$ is one more than the dimension of $Z$. Let $\omega_Z$ denote the total space of the canonical line bundle of $Z$, considered as a non-compact Calabi–Yau variety. We use the theory of exceptional collections to describe t-structures on the derived category of coherent sheaves on $\omega_Z$. The combinatorics of these t-structures is determined by a natural action of an affine braid group, closely related to the well-known action of the Artin braid group on the set of exceptional collections on $Z$.