### Abstract

We study hypersurfaces of $${\mathbb{C}}-{n+2}_{{\bar x},u,v}$$ given by equations of form $$UV = P({\bar X})$$ where the zero locus of a polynomial p is smooth reduced. The main result says that the Lie algebra generated by algebraic completely integrable vector fields on such a hypersurface coincides with the Lie algebra of all algebraic vector fields. Consequences of this result for some conjectures of affine algebraic geometry and for the Oka-Grauert-Gromov principle are discussed.

Original language | English (US) |
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Pages (from-to) | 115-131 |

Number of pages | 17 |

Journal | Mathematische Zeitschrift |

Volume | 258 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2008 |

### Keywords

- Affine space
- Andersén-Lempert- theory
- Density property
- Oka-Grauert-Gromov principle

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Kaliman, S., & Kutzschebauch, F. (2008). Density property for hypersurfaces UV = P(X̄).

*Mathematische Zeitschrift*,*258*(1), 115-131. https://doi.org/10.1007/s00209-007-0162-z