Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T23:06:53.386Z Has data issue: false hasContentIssue false
  • English
  • Français

On the theta divisor of SU(r; 1)

Published online by Cambridge University Press:  22 January 2016

Sonia Brivio  and
Alessandro Verra
Sonia Brivio
Affiliation:
Dipartimento di Matematica, Universita’ di Pavia, via Abbiategrasso, 209 - 27100 Pavia, Italy, [email protected]
Alessandro Verra
Affiliation:
Dipartimento di Matematica, Universita’ di Roma Tre, largo S. Leonardo Murialdo 1 - 00146, Roma, Italy, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let SU(r; 1) be the moduli space of stable vector bundles, on a smooth curve C of genus g ≥ 2, with rank r ≥ 3 and determinant OC(p), p ∈ C; let L be the generalized theta divisor on SU(r; 1). In this paper we prove that the map øL, defined by L, is a morphism and has degree 1.

Keywords

14D20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 165 , March 2002 , pp. 179 - 193
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[A-C-G-H] Arbarello, E. Cornalba, M., Griffiths, P.A. and Harris, J., Geometry of Algebraic curves, Springer verlag, Berlin, 1985.Google Scholar
[Be1] Beauville, A., Fibres de rang 2 sur une courbe, fibre determinant et functions theta, Bull. Soc.Math.France, 116 (1988), 431–448.CrossRefGoogle Scholar
[Be2] Arbarello, E. Cornalba, M., Griffiths, P.A. and Harris, J., Fibres de rang 2 sur une courbe, fibre determinant et functions theta II, Bull. Soc. Math.France, 119 (1991), 259–291.Google Scholar
[B] Brivio, S., On the degeneracy locus of a map of vector bundles on Grassmannian Varieties, Preprint (1999).Google Scholar
[B-V1] Brivio, S. and Verra, A., The theta divisor of SUC(2)S is very ample if C is not hyperelliptic, Duke Math. J., 82 (1996), 503–552.Google Scholar
[B-V2] Brivio, S. and Verra, A., On the theta divisor of SU(2,1), Int. J. math., 10, 8 (1998), 925–942.Google Scholar
[D-N] Drezet, I.M. and Narasimhan, M.S., Groupes de Picard des variétés des modules desfibres semistable sur les courbes algebriques, Invent.Math., 97 (1989), 53–94.CrossRefGoogle Scholar
[D-R] Desale, U.V. and Ramanan, S., Classificationn of vector bundles of rank two on hyperelliptic curves, Invent. Math., 38 (1976), 161–185.Google Scholar
[H] Hartshorne, R., Algebraic Geometry, Springer verlag, New York, 1977.CrossRefGoogle Scholar
[I-vG] zadi, E.I and Geemen, L. van, The tangent space to the moduli space of vector bunldes on a curve and the singular locus of the theta divisor of the Jacobian, Preprint (1997).Google Scholar
[L] Laszlo, Y., A propos de lespace des modules de fibres de rang 2 sur une courbe, Math. Ann., 299 (1994), 597–608.CrossRefGoogle Scholar
[N-R] Narasimhan, M.S. and Ramanan, S., Moduli of vector bundles on a compact Riemann surface, Ann.Math., 89 (1969), 19–51.Google Scholar
[N] Newstead, P.E., Rationality of moduli spaces of vector bundles over an algebraic curve, Math.Ann., 215 (1975), 251–268. Correction, ibidem, 249, (1980), 281–282.Google Scholar
[Ra] Ramanan, S., The moduli spaces of vector bundles over an algebraic curve, Math. Ann., 200 (1973), 69–84.CrossRefGoogle Scholar
[R] Raynaud, M., Sections des fibrès vectoriels sur une courbe, Bull.Soc.math. France, 110 (1982), 103–125.Google Scholar
[S] Seshadri, C.S., Fibrès vectoriels sur les courbes algèbriques, Astèrisque, 96 (1982), 3–50.Google Scholar