manuscripta mathematica

, Volume 52, Issue 1–3, pp 63–80

Höhere Sekantenvarietäten und Vektorbündel auf Kurven

  • Herbert Lange
Article

Abstract

If E denotes a vector bundle of rank 2 an a smooth projective curve X, an upper bound for the number m(E) of sublinebundles of maximal degree of E is given in terms of the genus of X and the invariant s(E). The proof is an application of an enumerative result for higher secant varieties of curves in projective space.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. [1]
    ARBARELLO, E., CORNALBA, M., GRIFFITHS, P., HARRIS, J.: Preprint on special divisors of curves, (1984)Google Scholar
  2. [2]
    BERZOLARI, L.: Palermo Rend. 9, 186 (1895)Google Scholar
  3. [3]
    FULTON, W.: Intersection Theory, Ergebnisse der Math. 2, Springer-Verlag, (1984)Google Scholar
  4. [4]
    GHIONE, F.: Quelques résulats de Corrado Segre sur les surfaces réglés, Math. Ann. 255, 77–95 (1981).Google Scholar
  5. [5]
    HARTSHORNE, R.: Algebraic Geometry, Graduate Texts in Math. 52, Springer Verlag, (1977)Google Scholar
  6. [6]
    LANGE, H., NARASIMHAN, M.S.: Maximal subbundles of rank 2 vector bundles on curves, Math. Ann. 266, 55–72 (1983)Google Scholar
  7. [7]
    LANGE, H.: Higher secant varieties of curves and the theorem of Nagata on ruled surfaces, manuscr, math. 47, 263–269 (1984)Google Scholar
  8. [8]
    MATTUCK, A.P.: Secant bundles on symmetric products, Am. J. Math. 87, 779–797 (1965)Google Scholar
  9. [9]
    SCHWARZENBERGER, R.L.E.: The secant bundle of a projective variety, Proc. J. London Math. 14, 369–384 (1964)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Herbert Lange
    • 1
  1. 1.Mathematisches InstitutUniversität Erlangen-NürnbergErlangen

Personalised recommendations