Skip to main content
SpringerLink
Log in

Explicit determination of the Picard group of moduli spaces of semistable G-bundles on curves

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Adams, F.: Lectures on Lie Groups. W. A. Benjamin, Inc., 1969

  2. Arbarello, E., Cornalba, M., Griffiths, P., Harris, J.: Geometry of Algebraic Curves. Springer-Verlag, 1985

  3. Beauville, A., Laszlo, Y.: Conformal blocks and generalized theta functions. Commun. Math. Phys. 164, 385–419 (1994)

    Google Scholar 

  4. Beauville, A., Laszlo, Y., Sorger, C.: The Picard group of the moduli of G–bundles on a curve. Compositio Math. 112, 183–216 (1998)

    Google Scholar 

  5. Beltrametti, M., Robbiano, L.: Introduction to the theory of weighted projective spaces. Expo. Math. 4, 111–162 (1986)

    Google Scholar 

  6. Bernshtein, I.N., Shvartsman, O.V.: Chevalley’s theorem for complex crystallographic Coxeter groups. Funct. Anal. Appl. 12, 308–310 (1978)

    Google Scholar 

  7. Bourbaki, N.: Groupes et Algèbres de Lie, Chap. 4–6. Masson, Paris, 1981

  8. Drezet, J.–M., Narasimhan, M.S.: Groupe de Picard des variétés de modules de fibrés semi–stables sur les courbes algébriques. Invent. Math. 97, 53–94 (1989)

    Google Scholar 

  9. Dynkin, E.B.: Semisimple subalgebras of semisimple Lie algebras. Am. Math. Soc. Transl. (Ser. II) 6, 111–244 (1957)

    Google Scholar 

  10. Faltings, G.: A proof for the Verlinde formula. J. Alg. Geom. 3, 347–374 (1994)

    Google Scholar 

  11. Friedman, R., Morgan, J.W., Witten, E.: Principal G-bundles over elliptic curves. Mathematical Research Letters 5, 97–118 (1998)

    Google Scholar 

  12. Fulton, W.: Intersection Theory. Springer, Berlin Heidelberg, 1998

  13. Knudsen, F., Mumford, D.: The projectivity of the moduli space of stable curves I: preliminaries on “det” and “div”. Math. Scand. 39, 19–55 (1976)

    Google Scholar 

  14. Kumar, S.: Infinite Grassmannians and moduli spaces of G–bundles. In: Vector Bundles on Curves - New Directions, Lecture Notes in Mathematics 1649, pp. 1–49, Springer, Berlin Heidelberg, 1997

  15. Kumar, S.: Kac-Moody Groups, their Flag Varieties and Representation Theory. Progress in Mathematics vol. 204, Birkhäuser, 2002

  16. Kumar, S., Narasimhan, M.S.: Picard group of the moduli spaces of G–bundles. Math. Annalen 308, 155–173 (1997)

    Google Scholar 

  17. Kumar, S., Narasimhan, M.S., Ramanathan, A.: Infinite Grassmannians and moduli spaces of G–bundles. Math. Annalen 300, 41–75 (1994)

    Google Scholar 

  18. Lang, S.: Introduction to Arakelov Theory. Springer, Berlin Heidelberg, 1988

  19. Laszlo, Y.: About G-bundles over elliptic curves. Ann. Inst. Fourier, Grenoble 48, 413–424 (1998)

    Google Scholar 

  20. Laszlo, Y., Sorger, C.: The line bundles on the moduli of parabolic G–bundles over curves and their sections. Ann. Scient. Éc. Norm. Sup. 30, 499–525 (1997)

    Google Scholar 

  21. Looijenga, E.: Root systems and elliptic curves. Invent. Math. 38, 17–32 (1976)

    Google Scholar 

  22. Milne, J.S.: Chap. VII–Jacobian varieties. In: Arithmetic Geometry, Cornell, G., et al., (eds.), Springer, Berlin Heidelberg 1986, 167–212

  23. Milnor, J.W., Stasheff, J.D.: Characteristic Classes. Annals of Mathematics Studies vol. 76, Princeton University Press, 1974

  24. Narasimhan, M.S., Seshadri, C.S.: Stable and unitary vector bundles on a compact Riemann surface. Ann. of Math. 82, 540–567 (1965)

    Google Scholar 

  25. Narasimhan, R.: Compact Riemann Surfaces. Birkhäuser Verlag, 1992

  26. Ramanan, S., Ramanathan, A.: Some remarks on the instability flag. Tôhoku Math. J. 36, 269–291 (1984)

    Google Scholar 

  27. Ramanathan, A.: Stable principal bundles on a compact Riemann surface- Construction of moduli space. Thesis, University of Bombay, 1976

  28. Ramanathan, A.: Stable principal bundles on a compact Riemann surface. Math. Ann. 213, 129–152 (1975)

    Google Scholar 

  29. Sorger, C.: On moduli of G-bundles on a curve for exceptional G. Ann. Scient. Éc. Norm. Sup. 32, 127–133 (1999)

    Google Scholar 

  30. Szenes, A.: The combinatorics of the Verlinde formulas In: Vector Bundles in Algebraic Geometry, Hitchin, N.J., et al., (eds.), Cambridge University Press, 1995

  31. Teleman, C.: Lie algebra cohomology and the fusion rules. Commun. Math. Phys. 173, 265–311 (1995)

    Google Scholar 

  32. Teleman, C.: Borel-Weil-Bott theory on the moduli stack of G-bundles over a curve. Invent. Math. 134, 1–57 (1998)

    Google Scholar 

  33. Tsuchiya, A., Ueno, K., Yamada, Y.: Conformal field theory on universal family of stable curves with gauge symmetries. Adv. Stud. Pure Math. 19, 459–565 (1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599-3250, USA

    Arzu Boysal & Shrawan Kumar

Authors
  1. Arzu Boysal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shrawan Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arzu Boysal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boysal, A., Kumar, S. Explicit determination of the Picard group of moduli spaces of semistable G-bundles on curves. Math. Ann. 332, 823–842 (2005). https://doi.org/10.1007/s00208-005-0655-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00208-005-0655-1

Keywords

Search

Navigation