2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147097We 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 suitable component $\hat X$ of the moduli space of stable sheaves on $X$. For a wide class of K3 surfaces $\hat X$ 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 $F$.Revised version, 15 pages AMSTeX with AMSppt.sty v. 2.1bAlgebraic Geometry14F05 (Primary), 32L07, 32L25, 58D27 (Secondary)text