Neighborhoods of a Compact Non-Singular Algebraic Curve Imbedded in a 2-Dimensional Complex Manifold

Abstract

Let C be a compact non-singular algebraic curve imbedded in a 2-dimensional complex manifold S. In this paper we consider the following problem: Under what conditions does there exist a non-constant holomorphic function defined on a small neighborhood of Cl The signature of the normal bundle Nc is not sufficient to solve our problem (see, Table in § 6 and Theorem 2 in § 5). Hence we have to introduce the concept of a regularly half pseudoconvex neighborhood system of C (for definition, see (1.1)). Then the necessary and sufficient condition is given in the following