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NON COMPACT BOUNDARIES OF COMPLEX ANALYTIC VARIETIES
 

Summary: NON COMPACT BOUNDARIES OF COMPLEX
ANALYTIC VARIETIES
GIUSEPPE DELLA SALA,
ALBERTO SARACCO
Abstract. We treat the boundary problem for complex varieties
with isolated singularities, which are contained in a certain class
of strongly pseudoconvex, not necessarily bounded open subsets of
Cn
.
1. Introduction
Let M be a smooth and oriented real (2m + 1)-submanifold of some
n-complex manifold X. A natural question arises, whether M is the
boundary of an (m + 1)-complex analytic subvariety of X. This prob-
lem, the so called boundary problem, has been widely treated over the
past fifty years when M is compact and X is Cn
or CPn
.
The case when M is a compact, connected curve in X = Cn
(m = 0),
has been first solved by Wermer [12] in 1958. Later on, in 1975, Harvey

  

Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa

 

Collections: Mathematics