Density property for hypersurfaces UV = P(X̄)

Shulim Kaliman, Frank Kutzschebauch

Research output: Contribution to journalArticle

27 Scopus citations

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 languageEnglish (US)
Pages (from-to)115-131
Number of pages17
JournalMathematische Zeitschrift
Volume258
Issue number1
DOIs
StatePublished - 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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