Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets

TL;DR

This paper constructs open Stein neighborhoods for certain compact sets in complex spaces, specifically those combining a holomorphically convex set and a complex curve with smooth boundary, even when they intersect.

Contribution

It introduces a method to create Stein neighborhoods for unions of holomorphically convex sets and complex curves with smooth boundaries in complex spaces.

Findings

Successfully constructs Stein neighborhoods for the union of a holomorphically convex set and a complex curve.

Handles intersections where the curve and set are $ ext{O}(A)$-convex.

Extends existing techniques to more general configurations in complex analysis.

Abstract

In this paper we construct open Stein neighbourhoods of compact sets of the form $A\cup K$ in a complex space, where $K$ is a compact holomorphically convex set, $A$ is a compact complex curve with boundary $bA$ of class $\mathscr C^2$ which may intersect $K$, and $A\cap K$ is $\mathscr O(A)$-convex.