Holomorphic Mappings between Real Analytic Submanifolds in Complex Space

摘要

;Contents: Prelinimaries on algebraic mappings and CR geometry (Algebraicmappings, Real analytic CR submanifolds in Cn, Finite type and minimality, Normal forms for generic submanifolds, The complexification of a real analytic submanifold); Holomorphic nondegeneracy, finite nondegeneracy, and reflection identifies for holomorphic mappings (Holomorphic nondegeneracy of real analytic CR submanifolds, Finite nondegeneracy of real analytic CR subminifolds, Reflection identities for holomorphic mappings); The Serge sets (The Serge sets of a real analytic CR submanifold, Homogeneous submanifolds of CR dimension 1, Proof of Teorem 4.1.21 (CR dimension 1 case)); An application to holomorphic mappings between real algebraic submanifolds (A reformulation of Theorem 1.1, Proof of Theorem 5.1.1); Other applications and concluding remarks (The algebraic equivalence problem, Uniqueness of biholomorphisms between real analytic, generic submanifolds).