Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-17T08:59:02.099Z Has data issue: false hasContentIssue false
  • English
  • Français

Hilbert schemes of points on some K3 surfaces and Gieseker stable bundles

Published online by Cambridge University Press:  24 October 2008

Ugo Bruzzo  and
Antony Maciocia
Ugo Bruzzo
Affiliation:
International School for Advanced Studies, Via Beirut 2-4, 34014 Miramare, Trieste, Italy e-mail address: bruzzo@sissa.it
Antony Maciocia
Affiliation:
Department of Mathematics and Statistics, The University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK e-mail address: ama@maths.ed.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

By using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfaces X the Hilbert schemes Hilbn(X) can be identified for all n ≥ 1 with moduli spaces of Gieseker stable vector bundles on X. We also introduce a new Fourier-Mukai type transform for such surfaces.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 2 , August 1996 , pp. 255 - 261
Copyright
Copyright © Cambridge Philosophical Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ballico, E. and Chantini, L.. On some moduli space of rank 2 bundles over K3 surfaces. Boll. U.M.I. 7-A (1993), 279–287.Google Scholar
[2]Bartocci, C., Bruzzo, U. and Ruipérez, D. Hernández. A Fourier–Mukai transform for stable bundles on K3 surfaces. Preprint DIMA 261/1994; Alg-Geom Preprint #9405006.Google Scholar
[3]Bartocci, C., Bruzzo, U. and Ruipérez, D. Hernández. Existence of µ-stables bundles on K3 surfaces and the Fourier–Mulai transform, preprint.Google Scholar
[4]Göttsche, L. and Huybrechts, D.. Hodge numbers of moduli spaces of stable bundles on K3 surfaces, preprint, M.P.I. (1994).CrossRefGoogle Scholar
[5]Maciocia, A.. The determinant line bundle over moduli spaces of instantons on abelian surfaces. Math. Z. 217 (1994), 317–333.CrossRefGoogle Scholar
[6]Maciocia, A.. Generalised Fourier–Mukai transforms, preprint (Edinburgh University, 1994).Google Scholar
[7]Mukai, S.. Duality between D(X) andD(X^) with its application to Picard sheaves. Nagoya Math. J. 81 (1981), 153–175.CrossRefGoogle Scholar
[8]Mukai, S.. On the moduli space of bundles on a K3 surface I; in Vector bundles on algebraic varieties (ed. Atiyah, M. F. et al. ), Tata Institute of Fundamental Research (Oxford University Press, 1987).Google Scholar
[9]Zuo, K.. The moduli spaces of some rank-2 stable vector bundles over algebraic K3-surfaces. Duke Math. J. 64 (1991), 403–408.CrossRefGoogle Scholar