The special McKay correspondence and exceptional collection

Abstract

We show that the derived category of coherent sheaves on the quotient stack of the affine plane by a finite small subgroup of the general linear group is obtained from the derived category of coherent sheaves on the minimal resolution by adding a semiorthogonal summand with a full exceptional collection. The proof is based on an explicit construction in the abelian case, together with the analysis of the behavior of the derived categories of coherent sheaves under root constructions.

23 pages, v2: major revision

References in corpus (2)

• Log Crepant Birational Maps and Derived Categories
• Smooth toric DM stacks

Cited by in corpus (5)

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• On graded stable derived categories of isolated Gorenstein quotient singularities