Perverse coherent sheaves and Fourier-Mukai transforms on surfaces

Details Perverse coherent sheaves and Fourier-Mukai transforms on surfaces Perverse coherent sheaves and Fourier-Mukai transforms on surfaces

2010-03-12

arxiv.org/abs/1003.2522v2

Mathematics

Algebraic Geometry

69 pages

Scientific paper

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.

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