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.

arXiv commentto appear in Invent. Math

Cited by in corpus (23)

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• Infinite transitivity on affine varieties
• Holomorphic families of non-equivalent embeddings and of holomorphic group actions on affine space
• Stein Spaces Characterized by their Endomorphisms
• Runge tubes in Stein manifolds with the density property
• Manifolds with infinite dimensional group of holomorphic automorphisms and the Linearization Problem
• A strong Oka principle for embeddings of some planar domains into CxC*
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• Infinite-dimensionality of the Automorphism Groups of Homogeneous Stein Manifolds
• The symplectic holomorphic density property for Calogero-Moser spaces
• Algebraic density property of homogeneous spaces
• (Volume) Density Property of a family of complex manifolds including the Koras-Russell Cubic
• Lie algebras of zero divergence vector fields on complex affine algebraic varieties
• Free dense subgroups of holomorphic automorphisms
• Algebraic (Volume) Density Property for Affine Homogeneous Spaces
• Extensions of isomorphisms of subvarieties in flexile varieties
• The density property for Gizatullin surfaces with reduced degenerate fibre