On framed instanton bundles and their deformations

We consider a compact twister space P and assume that there is a surface S subset of P, which has degree one on twister fibres and contains a twister fibre F, e. g. P a LeBrun twister space ([20], [18]). Similar to [6] and [5 ] we examine the restriction of an instanton bundle V equipped with a fixed trivialization along F to a framed vector bundle over (S, F). First we dev elope inspired by [13] a suitable deformation theory for vector bundles ove r an analytic space framed by a vector bundle over a subspace of arbitrary codimension. In the second section we describe the restriction as a smooth natural transformation into a fine moduli space. By considering framed U(r) -instanton bundles as a real structure on framed instanton bundles over P, we show that the bijection between isomorphism classes of framed U(r)-insta nton bundles and isomorphism classes of framed vector bundles over (S, F) d ue to [5] is actually an isomorphism of moduli spaces.