Seminar Algebra and Geometry: Alexandre Ramos Peon (Universität Bern)

Parametrized automorphisms of manifolds with the density property

As has been discussed recently in this seminar, manifolds with the "density property" have a particularly rich group of holomorphic automorphisms. In particular this group acts infinite-transitively on the manifold. This can be generalized as follows: if instead of this static state, we allow the configuration of finitely many points to vary in a holomorphic fashion, then there exists a "holomorphically depending" family of automorphisms, mapping, for each parameter, the corresponding configuration to a pre-defined tuple of points on the manifold. This is not trivial even in the affine case. The aim of the talk is to  introduce the notions and tools required, and of course to sketch a proof of a precise version of this theorem.

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