Seminar Algebra and Geometry: Rafael Andrist (Universität Wuppertal)

Holomorphic automorphisms of Danielewski surfaces

A Danielewski surface is given as the hypersurface $x y = f(z)$ in $\mathbb{C}^3$, where $f$ is a polynomial with only simple zeroes. Such a surface enjoys the Density Property, i.e. the Lie algebra generated by the complete holomorphic vector fields is dense in the Lie algebra of all holomorphic vector fields.

In case of a Danielewski surface the so-called overshear group is dense in the group of holomorphic automorphisms. We describe the group structure of the overshear group with the help of Nevanlinna theory.

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