Holomorphic hulls in terms of curves of nonnegative divisors and generalized polynomial hulls

Abstract

This paper is devoted to the study of the Basner hulls of compact subsets of C N. The principal result is a characterization of these hulls in terms of continuous families of varieties analogous to a well known characterization of polynomially convex hulls. This result is based on recent work of the authors concerning continuous families of divisors. In this paper we a apply a description of polynomial hulls in terms of "di- vergent curves of nonnegative divisors", which follows from the work (LS) and which is closely related to work of Oka and Stolzenberg (see (Sz) p. 263)) to obtain some information about certain generalized polynomial hulls introduced by Basner (Bs), in particular a description of these hulls in terms of one-parameter continuous families of polynomial maps. We shall also discuss some related properties of divergent curves of nonnegative divisors on Stein manifolds. The work depends in an essential way on the work in (LS) about solutions