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.
1997
486
1
16
https://arxiv.org/abs/alg-geom/9405006
Bartocci, C.; Bruzzo, U; Hernandez-Ruiperez, D.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14344
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 25
  • ???jsp.display-item.citation.isi??? 25
social impact