Journal of the Australian Mathematical Society

Research Article

VECTOR BUNDLES OVER A NONDEGENERATE CONIC

INDRANIL BISWASa1 c1 and D. S. NAGARAJa2

a1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India (email: indranil@math.tifr.res.in)

a2 The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India (email: dsn@imsc.res.in)

Abstract

Let k be a field and X a k-form of the projective line. We classify all the isomorphism classes of vector bundles over X.

(Received June 12 2007)

(Accepted December 12 2007)

2000 Mathematics subject classification

  • primary 14H60; secondary 14F05

Keywords and phrases

  • conic;
  • vector bundle;
  • Harder–Narasimhan filtration

Correspondence:

c1 For correspondence; e-mail: indranil@math.tifr.res.in

Footnotes

The second-named author would like to thank the CNRS for support.