Perverse coherent sheaves and Fourier-Mukai transforms on surfaces

TL;DR

This paper explores the role of perverse coherent sheaves on surface resolutions, demonstrating their connection to Fourier-Mukai transforms and extending duality theories for K3 surfaces.

Contribution

It introduces the application of perverse coherent sheaves to Fourier-Mukai transforms on surfaces, generalizing duality for K3 surfaces.

Findings

Perverse coherent sheaves appear naturally in Fourier-Mukai transform theory.

Generalization of Fourier-Mukai duality for K3 surfaces.

Examples on moduli spaces of stable sheaves on K3 and elliptic 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.