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

Bernhard Lamel (1) , Nordine Mir (2)

1 Fakultät für Mathematik [Wien]
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

We consider (small) algebraic deformations of germs of real-algebraic CR 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.

Mots clés: Holomorphic equivalence; Algebraic equivalence; CR manifold; CR orbits

Domaines: Variables complexes [math.CV]

Bernhard Lamel, Nordine Mir. Holomorphic versus algebraic equivalence for deformations of real-algebraic Cauchy-Riemann manifolds. Communications in Analysis and Geometry, 2010, 18 (5), pp.891-926. ⟨hal-00597019⟩