Cohomologie équivariante de [formula omitted] et application de Kirwan

Abstract

Let X be a holomorphic curve of genus g and m the moduli space of rank n degree k stable holomorphic bundles on X with fixed determinant, n⩾2, (n,k)=1 . We generalize the construction given in [4], when n=2, k=1 , of a universal bundle on X× m . The space m can be seen as a quasi-Hamiltonian reduction of the quasi-Hamiltonian space SU (n) 2g . Using our construction of the universal bundle, we give some results about the image of the equivalent of the Kirwan map for quasi-Hamiltonian spaces, the strongest results being when n=2.