Monatshefte für Mathematik

, Volume 146, Issue 4, pp 333–339 | Cite as

On Some Moduli Spaces of Bundles on K3 Surfaces

  • C. G. Madonna
Article

Abstract.

We give infinitely many examples in which the moduli space of rank 2 H-stable sheaves on a K3 surface S endowed by a polarization H of degree 2g – 2, with Chern classes c1 = H and c2 = g – 1, is birationally equivalent to the Hilbert scheme S[g – 4] of zero dimensional subschemes of S of length g – 4. We get in this way a partial generalization of results from [5] and [1].

2000 Mathematics Subject Classifications: 14J60 
Key words: Moduli of vector bundles, K3 surfaces, Hilbert schemes 

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References

  1. Ballico, E, Chiantini, L 1993On some moduli spaces of rank 2 bundles over K3 surfaces.Boll Un Mat Ital A7279287MathSciNetGoogle Scholar
  2. Beauville, A 1983Variétés kählériennes dont la première classe de Chern est nulle.J Diff Geom18755782MATHMathSciNetGoogle Scholar
  3. Friedman, R 1995Vector bundles and SO(3)-invariants for elliptic surfaces.J Amer Math Soc829139MATHMathSciNetGoogle Scholar
  4. Huybrechts D, Lehn M (1997) The Geometry of Moduli spaces of Sheaves. Braunschweig: ViewegGoogle Scholar
  5. Madonna, C, Nikulin, VV 2003On a classical correspondence between K3 surfaces.Proc Steklov Math Inst241120153MathSciNetGoogle Scholar
  6. Mukai, S 1987On the moduli space of bundles on K3 surfaces. I. In: Vector Bundles on Algebraic Varieties.Tata Inst Fund Res, Studies Math11341413MATHMathSciNetGoogle Scholar
  7. Mukai, S 1984Symplectic structure of the moduli space of sheaves on an Abelian or K3 surface.Invent Math77101116MATHMathSciNetGoogle Scholar
  8. O’Grady, K 1997The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface.J Algebraic Geom6599644MathSciNetGoogle Scholar
  9. Yoshioka K (1999) Irreducibility of moduli spaces of vector bundles on K3 surfaces. Preprint math. AG/9907001Google Scholar
  10. Tyurin, AN 1988Special 0-cycles on a polarized K3 surface.Math USSR Izv30123143CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag/Wien 2005

Authors and Affiliations

  • C. G. Madonna
    • 1
  1. 1.Università degli Studi Roma “La Sapienza”Italia

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