Bemerkungen zur Deformationstheorie nichtrationaler Singularitäten

Let be a 1-convex holomorphic mapping between complex spaces resp.S, and let be the blowingdown factorization of over S. We prove in part 1 of the present note: The fiber ^–1(s₀) over a point s₀S is the Remmert quotient of if and only if every holomorphic function on (defined in a neighborhood of the exceptional subvariety of that fiber) can be extended holomorphically to . This is true, for instance, in the case: flat, S reduced at s₀ and dim , =const for all sS. In part 2, we use this result to obtain the following: For any Riemann surface R with genus g2 there exists a 2-dimensional normal complex analytic singularity X such that the minimal resolution of X contains R as exceptional subvariety, and has a deformation over the unit disc S={|s|<1} which can not be blown down to a deformation of X.