On moduli of vector bundles on rational surfaces (Q1087598)

Here the following theorem is proved: For every smooth, rational, projective surface (over \({\mathbb{C}})\) and ''many'' ample line bundles H and every \(r,c_ 1,c_ 2\), the moduli scheme \(M_ H(r,c_ 1,c_ 2)\) of rank-r H-stable vector bundles on S with Chern classes \(c_ i\) is irreducible and unirational (or empty).