Perverse coherent sheaves and Fourier–Mukai transforms on surfaces, II

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 appear in the theory of Fourier–Mukai transforms. As an application, we generalize the Fourier–Mukai duality for K3 surfaces to our situation.