Holomorphic separation and the union problem

Vigna Suria, Giuseppe

doi:10.1090/S0002-9939-1984-0760941-3

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Holomorphic separation and the union problem
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by Giuseppe Vigna Suria PDF

Proc. Amer. Math. Soc. 92 (1984), 538-540 Request permission

Abstract:

We give a sufficient condition for an increasing union of holomorphically separated analytic spaces to be holomorphically separated. Furthermore, an example of J. E. Fornaess is investigated in order to show that a union as above is not always holomorphically separated.

References

Aldo Andreotti and Hans Grauert, Théorème de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193–259 (French). MR 150342, DOI 10.24033/bsmf.1581
John Erik Fornaess, $2$ dimensional counterexamples to generalizations of the Levi problem, Math. Ann. 230 (1977), no. 2, 169–173. MR 486625, DOI 10.1007/BF01370661