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arXiv · 2112.14452

Semi-orthogonal decomposition and smoothing

Yujiro Kawamata
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Abstract

We investigate the behavior of semi-orthogonal decompositions of bounded derived categories of singular varieties under flat deformations to smooth varieties. We consider a Q-Gorenstein smoothing of a surface with a quotient singularity, and prove that a pretilting sheaf, which is constructed from a non-commutative deformation of a divisorial sheaf and generates a semi-orthogonal component of a bounded derived category, deforms to a direct sum of exceptional vector bundles which are mutually totally orthogonal.

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Yujiro Kawamata. 2021-12-29. Semi-orthogonal decomposition and smoothing. https://arxiv.org/abs/2112.14452

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