Déformations des extensions larges de faisceaux

Jean-Marc Drézet

Vol. 220 (2005), No. 2, 201–297

DOI: 10.2140/pjm.2005.220.201

Abstract

Let X be a projective smooth irreducible polarized variety over the field of complex numbers. Typical examples of wide extensions are vector bundles E that have a subsheaf F whose slope is much bigger than the slope of E∕F, and such that F and E∕F are stable. We study the deformations of such bundles. The case of unstable rank 2 bundles has been considered by S. A. Strømme on ℙ₂, and by C. Bănică on ℙ₃. We build moduli spaces of wide extensions, and if the dimension of X is greater than 2, it may even happen that we obtain fine moduli spaces.

Keywords

deformations, moduli, unstable sheaves

Mathematical Subject Classification 2000

Primary: 14D20

Milestones

Received: 20 September 2003

Accepted: 8 February 2005

Published: 1 June 2005