Arkiv för Matematik

Volume 60 (2022)

Number 2

Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets

Pages: 335 – 349



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


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.


Stein manifold, complex curve, holomorphically convex set

2010 Mathematics Subject Classification

32E10, 32E20, 32U05

The author’s research was supported in part by the research program P1-0291 and grants J1-9104 and J1-3005 from ARRS, Republic of Slovenia.

Received 20 April 2021

Received revised 11 March 2022

Accepted 22 March 2022

Published 26 October 2022