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T-structures on some local Calabi-Yau varieties

Tom Bridgeland
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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 $ω_Z$ 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 $Z$.

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Tom Bridgeland. 2005-02-02. T-structures on some local Calabi-Yau varieties. https://arxiv.org/abs/math/0502050

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