T-structures on some local Calabi–Yau varieties

Abstract

Let Z be a smooth Fano variety satisfying the condition that the rank of the Grothendieck group of Z is one more than the dimension of Z. Let ω 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 ω 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.