Perverse coherent sheaves and Fourier-Mukai transforms on surfaces

Abstract

We study perverse coherent sheaves on the resolution of rational double points. As examples, we consider rational double points on 2-dimensional moduli spaces of stable sheaves on K3 and elliptic surfaces. Then we show that perverse coherent sheaves appears in the theory of Fourier-Mukai transforms. As an application, we generalize the Fourier-Mukai duality for K3 surfaces to our situation.

arXiv comment69 pages

Cited by in corpus (3)

• Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland's stability conditions
• Moduli spaces of stable sheaves on Enriques surfaces
• T-structures on elliptic fibrations