A ug 1 99 6 A FOURIER-MUKAI TRANSFORM FOR STABLE BUNDLES ON K 3 SURFACES

@inproceedings{Bartocci1996AU1,
  title={A ug 1 99 6 A FOURIER-MUKAI TRANSFORM FOR STABLE BUNDLES ON K 3 SURFACES},
  author={Claudio Bartocci and U. Bruzzo and D. Hern{\'a}ndez Ruip{\'e}rez},
  year={1996}
}
We define a Fourier-Mukai transform for sheaves on K3 surfaces over C, and show that it maps polystable bundles to polystable ones. The rôle of " dual " variety to the given K3 surface X is here played by a suitable component X of the moduli space of stable sheaves on X. For a wide class of K3 surfaces X can be chosen to be isomorphic to X; then the Fourier-Mukai transform is invertible, and the image of a zero-degree stable bundle F is stable and has the same Euler characteristic as F . 
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