Skip to main content
Log in

Generalized SU(2) theta functions

  • Published:
Inventiones mathematicae Aims and scope

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

  • [AB] Atiyah, M.F., Bott, R.: Yang-Mills equations over Riemann surfaces. Philos. Trans. R. Soc. Lond.308, 523–615 (1982)

    Google Scholar 

  • [B1] Bertram, A.: Moduli of rank-2 vector bundles, theta divisors, and the geometry of curves in projective space. J. Differ. Geom.35, 429–470 (1992)

    Google Scholar 

  • [B2] Bertram, A.: Stable pairs and stable parabolic pairs on curves. (Preprint 1992)

  • [Bo] Bott, R.: Stable bundles revisited. Surv. Differ. Geom1, 1–18 (1991)

    Google Scholar 

  • [BD] Bradlow, S., Daskalopoulos, G.: Moduli of stable pairs for holomorphic bundles over Riemann surfaces. Int. J. Math.2 (no. 5), 477–513 (1991)

    Google Scholar 

  • [BS] Bertram, A., Szenes, A.: Hilbert Polynomials of moduli spaces of rank 2 vector bundles. II. (Preprint 1991)

  • [D] Donaldson, S.K.: Polynomial invariants for smooth four-manifolds. Topology29, 257–315 (1990)

    Google Scholar 

  • [DN] Drezet J.M., Narasimhan, M.S.: Groupe de Picard des variétés de fibrés semistables sur les courbes algébriques. Invent. Math.97, 53–94 (1989)

    Google Scholar 

  • [DW] Daskalopoulos, G., Wentworth, R.: Geometric quantization for the moduli space of vector bundles with parabolic structure. (Preprint 1991)

  • [G] Gieseker, D.: Geometric invariant theory and applications to moduli problems. In: Gherardelli, F. (ed.) Invariant theory. (Lect. Notes Math., vol. 996, pp. 45–73, Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  • [H] Hartshorne, R.: Algebraic Geometry. (Grad. Texts Math., vol. 52) Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  • [Hi] Hirschowitz, A.: Problems de Brill-Noether en rang superieur. C.R. Acad. Sci., Paris, Ser I 307, 153–156 (1988)

    Google Scholar 

  • [Hit] Hitchin, N.J. Flat connections and geometric quantization. Commun. Math. Phys.131, 347–380 (1990)

    Google Scholar 

  • [M] Mumford, D.: Towards an enumerative geometry of the moduli space of curves. In: Artin, M., Tate, J. (eds.) Arithmetic and Geometry (dedicated to I.R Shafarevich), vol. II (Prog. Math. vol. 36) Boston Basel Stuttgart: Birkhäuser 1983

    Google Scholar 

  • [MS] Mehta V.B., Seshadri, C.S.: Moduli of vector bundles on curves with parabolic structures. Math. Ann.248, 205–239 (1980)

    Google Scholar 

  • [NR] Narasimhan, M.S., Ramanan, S.: Deformations of the moduli space of vector bundles over an algebraic curve. Ann. Math.101, 391–417 (1975)

    Google Scholar 

  • [NRs] Narasimhan M.S., Ramadas, T.R.: Factorisation of generalized theta functions. I. (Preprint 1992)

  • [NS] Narasimhan M.S., Seshadri, C.S.: Stable and unitary vector bundles on a compact surface. Ann. Math.82, 540–567 (1965)

    Google Scholar 

  • [R] Ramanan, S.: The moduli spaces of vector bundles over an algebraic curves. Math. Ann.200, 69–84 (1973)

    Google Scholar 

  • [S] Seshadri, C.S.: Fibrés Vectoriels sur les Courbes Algébriques. (Lectures at the E.N.S., notes by J.M. Drezet). Astérisque96 (1982)

  • [SS] Schiffman, B., Sommese, A.: Vanishing Theorems on Complex Manifolds. (Prog. Math., vol. 56) Boston Basel Stuttgart. Birkhäuser 1985

    Google Scholar 

  • [Sz] Szenes, A.: Hilbert polynomials of moduli spaces of rank 2 vector bundles. I. (Preprint 1991)

  • [T1] Thaddeus, M.: Stable pairs, linear systems and the Verlinde formula. Thesis, Oxford (1992)

  • [T2] Thaddeus, M.: Conformal field theory and the cohomology of the moduli space of stable bundles. J. Differ. Geom.35, 131–149 (1992)

    Google Scholar 

  • [V] Verlinde, E.: Fusion rules and modular transformations in 2d conformal field theory. Nucl. Phys.B 300, 360–376 (1988)

    Google Scholar 

  • [Z] Zagier, D.: The cohomology ring of the moduli space of rank 2 vector bundles (in preparation)

Download references

Author information

Authors and Affiliations

Authors

Additional information

Oblatum 12-VI-1991 & 8-IX-1992

Research in part supported by NSF postdoctoral research fellowship DMS-89-05510

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bertram, A. Generalized SU(2) theta functions. Invent Math 113, 351–372 (1993). https://doi.org/10.1007/BF01244310

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01244310

Keywords

Navigation