Skip to main content
Log in

Local structure of the moduli space of vector bundles over curves

  • Published:
Commentarii Mathematici Helvetici

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [B-N-R]A. Beauville, M. S. Narasimhan andM. S. Ramanan,Spectral curves and the generalized theta divisor, J. reine angew. Math.398 (1989) 169–179.

    MathSciNet  Google Scholar 

  • [B]J. F. Boutot,Singularites rationelles et quotients par les groupe reductifs, Inv. Math.88 (1987) 65–68.

    Article  MathSciNet  Google Scholar 

  • [C]A. B. Coble,Algebraic geometry and Theta functions, Amer. Math. Soc. (1929).

  • [D-N]J. M. Drezet andM. S. Narasimhan,Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques, Invent. Math.97 (1989) 53–94.

    Article  MathSciNet  Google Scholar 

  • [D-O]I. Dolgacev andD. Ortland,Point set in projective spaces and theta functions, Astéisque,165 (1988).

  • [EGA IV]A. Grothendieck,Elements de géométrie algébrique, avec la collaboration de J. Dieudonne, Publ. Math. I.H.E.S.24 (1965).

  • [F]W. Fulton,Intersection theory, Ergeb. der Math. und ihrer Grenzgebiete, 3. Folge Band 2, Springer-Verlag, Berlin Heidelberg New York Tokyo (1984).

    MATH  Google Scholar 

  • [H-R]M. Hochster, J. Roberts,Rings of invariants of reductive groups acting on regular local rings are Cohen-Macaulay, Adv. in Math.13 (1974) 115–175.

    Article  MathSciNet  Google Scholar 

  • [H-T]J. Harris andL. W. Tu,On symmetric and skew symmetric determinantal varieties, Topology23 (1984) 71–84.

    Article  MathSciNet  Google Scholar 

  • [Ha]R. Hartshorne,Algebraic Geometry, GTM 52, Springer Verlag, Berlin-Heidelberg-New York (1977).

    MATH  Google Scholar 

  • [J]T. Jozefiak,Ideals generated by minors of a symmetric matrix, Comment. Math. Helvetici53 (1978) 595–607.

    Article  MathSciNet  Google Scholar 

  • [Kh1]A. Khaled,Projective normality and equations of Kummer varieties, J. reine angew. Math.465 (1995), 197–217.

    MathSciNet  Google Scholar 

  • [Kh2]A. Khaled,Equations des variétés de Kummer, Math. Annal.295 (1993) 685–701.

    Article  MathSciNet  Google Scholar 

  • [Ko]S. Koizumi,Theta relations and projective normality of Abelian varieties, Amer. Journ. of Math.98 (1976) 865–889.

    Article  MathSciNet  Google Scholar 

  • [La]Y. Laszlo,Un théorème de Riemann pour les diviseurs Thêta généralisés sur les espaces de modules de fibrés stables sur une courbe, Duke Math. Journ.64 (1991) 333–347.

    Article  MathSciNet  Google Scholar 

  • [LeB]L. Le Bruyn,Trace rings of generic 2 by 2 matrices, Mem. A.M.S.66 (1987).

  • [Lu]D. Luna,Slices étales, Mém. Soc. Math. France33 (1973) 81–105.

    Google Scholar 

  • [M]D. Mumford,On equations defining Abelian varieties, Invent. Math.1 (1966) 287–354.

    Article  MathSciNet  Google Scholar 

  • [N-R1]M. S. Narasimhan andM. S. Ramanan,Moduli of vector bundles on a compact Riemann surface, Ann. of Math.89 (1969) 14–51.

    Article  MathSciNet  Google Scholar 

  • [N-R2]M. S. Narasimhan andM. S. Ramanan,20-linear system on abelian varieties, inVector bundles and algebraic varieties, Oxford University Press, (1987) 415–427.

  • [P]C. Procesi,The invariant theory of n by n matrices, Adv. in Math.19, 306–381.

  • [Ras]J. Rasmyslev,Trace identities of full matrix algebras over a field of characteristic zero, Izv. Akad. Nauk. U.S.S.R.8 (1974) 727–760.

    Google Scholar 

  • [Ray]M. Raynaud,Sections des fibŕs vectoriels sur une courbe, Bull. Soc. Math. France110 (1982) 103–125.

    MathSciNet  Google Scholar 

  • [S]C. S. Seshadri,Fibrés vectoriels sur les courbes algébriques (rédigé par J. M. Drezet), Astérique96 (1982).

  • [W]H. Weyl,The classical groups, Princeton Univ. Press, Princeton, N.J. (1946).

    MATH  Google Scholar 

  • [W]H. Wirtinger,Untersuchung über thetafunctionen, Teubner, Leipzig (1935).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The author was partially supported by the European Science Project “Geometry of Algebraic Varieties”, Contract no. SCI-0398-C(A).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Laszlo, Y. Local structure of the moduli space of vector bundles over curves. Commentarii Mathematici Helvetici 71, 373–401 (1996). https://doi.org/10.1007/BF02566426

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02566426

Keywords

Navigation