Criteria for the density property of complex manifolds

Abstract

In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Andersén-Lempert result and to establish (almost free of charge) the algebraic density property for all linear algebraic groups whose connected components are different from tori or $\C_+$. As another application of this approach we tackle the question (asked among others by F. Forstnerič) about the density of algebraic vector fields on Euclidean space vanishing on a codimension 2 subvariety.

to appear in Invent. Math

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• Free dense subgroups of holomorphic automorphisms
• Lie algebras of zero divergence vector fields on complex affine algebraic varieties
• (Volume) Density Property of a family of complex manifolds including the Koras-Russell Cubic