A FOURIER-MUKAI TRANSFORM FOR STABLE BUNDLES ON K-3 SURFACES

We define a Fourier-Mukai transform for sheaves on K3 surfaces over C, and show that it maps polystable bundles to polystable ones. The role of ''dual'' variety to the given K3 surface X is here played by a sui table component X of the moduli space of stable sheaves on X. For a wi de class of K 3 surfaces X can be chosen to be isomorphic to X; then t he Fourier-Mukai transform is invertible, and the image of a zero-degr ee stable bundle F is stable and has the same Euler characteristic as F.