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

Abstract

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.