Communications in Analysis and Geometry

Volume 18 (2010)

Number 5

Holomorphic versus algebraic equivalence for deformations of real-algebraic Cauchy–Riemann manifolds

Pages: 891 – 925

DOI: http://dx.doi.org/10.4310/CAG.2010.v18.n5.a2

Authors

Bernhard Lamel (Fakultät für Mathematik, Universität Wien, Austria)

Nordine Mir (Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, Saint Etienne du Rouvray, France)

Abstract

We consider (small) algebraic deformations of germs of real-algebraic Cauchy–Riemann submanifolds in complex space and study the biholomorphic equivalence problem for such deformations. We show that two algebraic deformations of minimal holomorphically nondegenerate real-algebraic CR submanifolds are holomorphically equivalent if and only if they are algebraically equivalent.

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