The number of functions defining complex analytical sets (Q1076855)

That every analytic subset Y of an n-dimensional Stein space X can be defined by n holomorphic functions was proved by \textit{O. Forster} and \textit{K. J. Ramspott} [Bayer. Akad. Wiss. Math.-Naturw. Kl., S.-ber. 1963, 89-99 (1964; Zbl 0123.271)]. And if X and Y are non-singular then there are n holomorphic functions which generate the ideal sheaf of Y at every point of Y [\textit{O. Forster}, Math. Z. 97, 376-405 (1967; Zbl 0148.322)]. In the present paper it is shown that there are n holomorphic functions defining an analytic subspace Y of an n-dimensional Stein manifold X such that these functions generate the ideal sheaf of Y at every regular point of Y. The proof uses the endromisbundle of \textit{O. Forster} and \textit{K. J. Ramspott} [Invent. Math. 2, 145-170 (1966; Zbl 0154.334)].