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 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.
A Fourier-Mukai transform for stable bundles on K3 surfaces / Bartocci, C.; Bruzzo, U; Hernandez-Ruiperez, D.. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - 486:(1997), pp. 1-16. [10.1515/crll.1997.486.1]
A Fourier-Mukai transform for stable bundles on K3 surfaces
Bruzzo, U;
1997-01-01
Abstract
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
