Arkiv för Matematik

Volume 60 (2022)

Number 2

Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets

Pages: 335 – 349

DOI: https://dx.doi.org/10.4310/ARKIV.2022.v60.n2.a6

Author

F. Forstnerič (Faculty of Mathematics and Physics, University of Ljubljana, Slovenia; and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia)

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 the set $A \cap K$ is $\mathscr{O}(A)$-convex.

Keywords

Stein manifold, complex curve, holomorphically convex set

2010 Mathematics Subject Classification

32E10, 32E20, 32U05

Received 20 April 2021

Received revised 11 March 2022

Accepted 22 March 2022

Published 26 October 2022