Semi-Orthogonal Decomposition and Smoothing
Vol. 31 (2024), No. 2, Page 127–165.
Kawamata, Yujiro
Semi-Orthogonal Decomposition and Smoothing
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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 $\mathbf Q$-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 weakly generates a semi-orthogonal component of a bounded derived category, deforms to a direct sum of exceptional vector bundles which are mutually totally orthogonal.
Keywords: Q-Gorenstein smoothing, derived category, semi-orthogonal decomposition, non-commutative deformation, exceptional vector bundle.
Mathematics Subject Classification (2020): 14B07, 14E30, 14J60.
Received: 2023-08-07
