Iterated Segre mappings of real submanifolds in complex space and applications

Abstract

This article is a survey of various applications of the method of iterated Segre mappings obtained by a number of mathematicians, including the author, over the past decade. This method is applied to various problems involving real submanifolds in complex space and their mappings. The article begins with a description of the iterated Segre mappings associated to generic submanifolds. The problems addressed concern transversality of holomorphic mappings, finite jet determination, local stability groups, and algebraicity of holomorphic mappings between real-algebraic manifolds.