Generic fibres on the projective plane (Q1317995)

The main result of this paper is a new proof of the irreducibility of the moduli spaces of stable vector bundles over the projective plane. Until now this study was done in four separate cases: (1) \(c_ 1 = 0\), \(\text{rk} = 2\) (W. Barth (1977)); (2) \(c_ 1 = - 1\), \(\text{rk} = 2\) (K. Hulek (1979) und G. Ellingsrud, S. A. Stromme (1979)); (3) \(c_ 1 = 0\), \(\text{rk} \geq 3\) (K. Hulek (1980)), (4) the remaining cases (G. Ellingsrud (1983)). Here the irreducibility follows from the general result that ``le champ'' (in the sense of G. Laumon, L. Moret-Baily) of ``prioritaire'' sheaves with fixed Hilbert polynomial is irreducible.