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Most real analytic Cauchy-Riemann manifolds are nonalgebraizable

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Abstract.

We give a simple argument to the effect that most germs of generic real analytic Cauchy-Riemann manifolds of positive CR dimension are not holomorphically embeddable into a generic real algebraic CR manifold of the same real codimension in a finite dimensional space. In particular, most such germs are not holomorphically equivalent to a germ of a generic real algebraic CR manifold.

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Authors and Affiliations

  1. Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Franc Forstnerič

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  1. Franc Forstnerič
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Correspondence to Franc Forstnerič.

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Mathematics Subject Classification (2000): Primary 32V20, 32V30

Supported in part by Research Program P1-0291, Republic of Slovenia

Acknowledgement I wish to thank Peter Ebenfelt and Alexander Sukhov for their invaluable advice concerning the state of knowledge on the question considered in the paper.

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Forstnerič, F. Most real analytic Cauchy-Riemann manifolds are nonalgebraizable. manuscripta math. 115, 489–494 (2004). https://doi.org/10.1007/s00229-004-0507-4

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  • DOI: https://doi.org/10.1007/s00229-004-0507-4

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