Semi-orthogonal decomposition and smoothing
arXiv:2112.14452
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.
30 pages, proof of Proposition 2.8 is corrected