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Density property for hypersurfaces \(UV = P({\bar X})\)

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Miami, Coral Gables, FL, 33124, USA

    Shulim Kaliman

  2. Mathematisches Institut, Universität Bern, Sidlerstr. 5, 3012, Bern, Switzerland

    Frank Kutzschebauch

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  1. Shulim Kaliman
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  2. Frank Kutzschebauch
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Correspondence to Shulim Kaliman.

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Kaliman, S., Kutzschebauch, F. Density property for hypersurfaces \(UV = P({\bar X})\) . Math. Z. 258, 115–131 (2008). https://doi.org/10.1007/s00209-007-0162-z

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  • DOI: https://doi.org/10.1007/s00209-007-0162-z

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