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 in Pic(Y ), H ample, with the following property. For any d in 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) = +∞.

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