The full exceptional collections of categorical resolutions of curves

Abstract

This paper gives a complete answer of the following question: which (singular, projective) curves have a categorical resolution of singularities which admits a full exceptional collection? We prove that such full exceptional collection exists if and only if the geometric genus of the curve equals to 0. Moreover we can also prove that a curve with geometric genus equal or greater than 1 cannot have a categorical resolution of singularities which has a tilting object. The proofs of both results are given by a careful study of the Grothendieck group and the Picard group of that curve.

10 pages, minor changes

Cited by in corpus (2)

• A Lie theoretical construction of a Landau-Ginzburg model without projective mirrors
• Scalar extensions of categorical resolutions of singularities