Advertisement

Archiv der Mathematik

, Volume 79, Issue 1, pp 74–80 | Cite as

Very ample vector bundles of curve genus two

  • H. Maeda
  • A. J. Sommese
Article

Abstract.

Let \( {\cal E} \) be a very ample vector bundle of rank n - 1 on a smooth complex projective variety X of dimension \( n \geqq 3 \), and let \( g(X, {\cal E}) \) be the curve genus of \( (X, {\cal E}) \) defined by the formula \( 2g(X, {\cal E}) - 2 = (K_{X} + c_{1}({\cal E}))c_{n-1}({\cal E})\), where KX is the canonical bundle of X. Then the pairs \( (X, {\cal E}) \) with \( g(X, {\cal E}) = 2 \) are classified.

Keywords

Vector Bundle Projective Variety Curve Genus Canonical Bundle Smooth Complex 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • H. Maeda
    • 1
  • A. J. Sommese
    • 2
  1. 1.Department of Mathematical Sciences, School of Science and Engineering, Waseda University,¶ 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan,¶e-mail: hmaeda@mse.waseda.ac.jpJapan
  2. 2.Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, U. S. A.,¶e-mail: sommese@nd.eduUSA

Personalised recommendations