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$$t$$-structures on some local Calabi–Yau varieties. (English) Zbl 1069.14044
Author’s 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 $$\omega_Z$$ 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 $$Z$$.

##### MSC:
 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 14J45 Fano varieties 18E30 Derived categories, triangulated categories (MSC2010)
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