The Michigan Mathematical Journal

Self-duality of Coble's quartic hypersurface and applications

Christian Pauly

Full-text: Open access

Article information

Michigan Math. J., Volume 50, Issue 3 (2002), 551-574.

First available in Project Euclid: 4 December 2002

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05]
Secondary: 14H40: Jacobians, Prym varieties [See also 32G20]


Pauly, Christian. Self-duality of Coble's quartic hypersurface and applications. Michigan Math. J. 50 (2002), no. 3, 551--574. doi:10.1307/mmj/1039029982.

Export citation


  • J. F. Adams, Lectures on exceptional Lie groups, Chicago Lectures in Mathematics, Univ. of Chicago Press, 1996.
  • A. Beauville, Fibrés de rang 2 sur une courbe, fibré déterminant et fonctions thêta, Bull. Soc. Math. France 116 (1988), 431--448.
  • ------, Fibrés de rang 2 sur une courbe, fibré déterminant et fonctions thêta II, Bull. Soc. Math. France 119 (1991), 259--291.
  • A. Beauville, Y. Laszlo, and C. Sorger, The Picard group of the moduli of $G$-bundles on a curve, Compositio Math. 112 (1998), 183--216.
  • A. B. Coble, Algebraic geometry and theta functions, Soc. Colloq. Publ., 10, Amer. Math. Soc., Providence, RI, 1929 (reprinted 1961).
  • I. Dolgachev and D. Ortland, Point sets in projective spaces and theta functions, Astérisque 165 (1988).
  • P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, New York, 1978.
  • S. Kleiman, Relative duality for quasi-coherent sheaves, Compositio Math. 41 (1980), 39--60.
  • F. Knudsen and D. Mumford, The projectivity of the moduli space of stable curves I, Math. Scand. 39 (1976), 19--55.
  • H. Lange and M. S. Narasimhan, Maximal subbundles of rank 2 vector bundles on curves, Math. Ann. 266 (1984), 55--72.
  • Y. Laszlo, Un théorème de Riemann pour les diviseurs Thêta généralisés sur les espaces de modules de fibrés stables sur une courbe, Duke Math. J. 64 (1994), 333--347.
  • ------, Local structure of the moduli space of vector bundles over curves, Comment. Math. Helv. 71 (1996), 373--401.
  • Y. Laszlo and C. Sorger, The line bundle on the moduli of parabolic $G$-bundles over curves and their sections, Ann. Sci. École Norm. Sup. (4) 30 (1997), 499--525.
  • Y. Manin, Cubic forms: Algebra, geometry, arithmetic, North-Holland, Amsterdam, 1974.
  • D. Mumford, Theta characteristics of an algebraic curve, Ann. Sci. École Norm. Sup. (4) 4 (1971), 181--192.
  • ------, Prym varieties I, Contributions to analysis (Ahlfors, Kra, Maskit, Niremberg, eds.), pp. 325--350, Academic Press, New York, 1974.
  • ------, Curves and their Jacobians, Univ. of Michigan Press, Ann Arbor, 1975.
  • M. S. Narasimhan and S. Ramanan, $2\theta$-linear system on abelian varieties, Vector bundles and algebraic varieties (Bombay, 1984), pp. 415--427, Oxford University Press, 1987.
  • W. M. Oxbury and C. Pauly, $SU(2)$-Verlinde spaces as theta spaces on Pryms, Internat. J. Math. 7 (1996), 393--410.
  • -----, Heisenberg invariant quartics and $SU_C(2)$ for a curve of genus four, Math. Proc. Cambridge Philos. Soc. 125 (1999), 295--319.
  • W. M. Oxbury, C. Pauly, and E. Previato, Subvarieties of $SU_C(2)$ and $2\theta$-divisors in the Jacobian, Trans. Amer. Math. Soc. 350 (1998), 3587--3617.