Analytic Sets and Complex Spaces

Abstract

Here we study the properties of singular analytic sets and complex spaces. The central theme of the first half of this chapter is “Oka’s Second Coherence Theorem”, claiming the coherence of a geometric ideal sheaf (the ideal sheaf of an analytic set). By making use of it, the subset of singular points of an analytic set is proved to be an analytic subset of lower dimension. In the latter half, the notion of a complex space is introduced. Oka’s normalization theorem, which reduces a singular point to a normal one with better property, and “Oka’s Third Coherence Theorem” claiming the coherence of the normalization sheaf are proved.