Criteria for the density property of complex manifolds

TL;DR

This paper introduces new criteria for the density property in complex manifolds, simplifying proofs and extending algebraic density results to broader classes of algebraic groups and vector fields.

Contribution

It provides effective criteria for the density property, simplifies existing proofs, and extends algebraic density results to certain linear algebraic groups and vector fields.

Findings

Simplified proof of the Andersén-Lempert theorem

Established algebraic density property for specific algebraic groups

Addressed density of algebraic vector fields vanishing on codimension 2 subvarieties

Abstract

In this paper we suggest new effective criteria for the density property. This enables us to give a trivial proof of the original Anders\'en-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. Forstneri\v{c}) about the density of algebraic vector fields on Euclidean space vanishing on a codimension 2 subvariety.