ABSTRACT
We refer to [GF], [GR] for generalities and details on complex spaces. Let U ⊂ Cn be an open set, and OU be the sheaf of holomorphic functions on U : for V open in U , by definition
OU (V ) = { f : V → C holomorphic } Then OU is a sheaf of local C-algebras. Theorem 7.1 (Oka’s theorem). The sheaf OU is coherent. Definition 7.1. A (complex) analytic subset of U ⊂ Cn is a closed subset S ⊂ U with the following property; for every x ∈ S there exist a neighborhood V of x in U and a finite number of holomorphic functions f1, . . . , fp on V such that S ∩ V = { z ∈ V ∣∣ f1(z) = · · · = fp(z) = 0}.
