Irreducibility and Connectivity. Extension of Analytic Sets

Abstract

In this chapter we are concerned with questions of connectivity of reduced complex spaces X and of residue spaces X \ A where A is thin in X. If X is connected such sets A may disconnect X as is shown by the standard example of a space consisting of two complex lines intersecting in a single point. Spaces for which this phenomenon cannot occur are called irreducible, we give different characterizations for such spaces (cf. Theorem 1.2). A basic role is played by the Global Decomposition Theorem 2.2. We demonstrate the power of this theorem by various applications in Sections 2 and 3.