Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets

Abstract: In this paper we construct open Stein neighbourhoods of compact sets of the form

A c u p K

in a complex space, where

K

is a compact holomorphically convex set,

A

is a compact complex curve with boundary

b A

of class

m a t h s c r C^{2}

which may intersect

K

, and

A c a p K

is

m a t h s c r O (A)

-convex.

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