Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces

Details Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces

1998-01-09

arxiv.org/abs/math/9801040v2

Mathematics

Complex Variables

12 pages An algorithm for finding complex-analytic discs in a real submanifold is added

Scientific paper

We prove that a germ of a holomorphic map $f$ between $C^n$ and $C^{n'}$
sending one real-algebraic submanifold $M\subset C^n$ into another $M'\subset
C^{n'}$ is algebraic provided $M'$ contains no complex-analytic discs and $M$
is generic and minimal. We also propose an algorithm for finding
complex-analytic discs in a real submanifold.

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