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On moduli of vector bundles on rational surfaces. (English) Zbl 0611.14008

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).

MSC:

14D20 Algebraic moduli problems, moduli of vector bundles
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14M20 Rational and unirational varieties
57R20 Characteristic classes and numbers in differential topology
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References:

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