Rank 2 vector bundles on higher dimensional projective manifolds

E. Ballico

Vol. 183 (1998), No. 1, 21–24

DOI: 10.2140/pjm.1998.183.21

Abstract

Fix a smooth complex projective n-fold X, n ≥ 5, with H¹(X,𝒪_X) = 0. Then there is a smooth projective n-fold Y birational to X and H ∈ Pic(Y ), H ample, with the following property. For any d ∈ Z let M(Y,2,𝒪,d,H) be the moduli scheme of H-stable rank 2 vector bundles, E, on Y with det(E)≅𝒪_Y and c₂(E) ⋅ Hⁿ⁻² = d. Let m(Y,2,𝒪,d,H) be the number of its irreducible components. Then limsup_d→∞m(Y,2,𝒪,d, H) = +∞.

Milestones

Received: 15 August 1996

Published: 1 March 1998