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the edit Finnur strangely did not make
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user5810
user5810

Fornaess and Stout proved that EVERY complex manifold (connected and second countable) can be covered by finitely many relatively compact open subsets biholomorphic to a polydisc (Lemma II.1 in MR0470251). They even have an explicit bound on the size of the cover in terms of the dimension of the manifold. Further results of a similar flavour are contained in their papers MR0435441 and MR0662439.

Fornaess and Stout proved that EVERY complex manifold (connected and second countable) can be covered by finitely many relatively compact open subsets biholomorphic to a polydisc (Lemma II.1 in MR0470251). They even have an explicit bound on the size of the cover in terms of the dimension of the manifold. Further results of a similar flavour are contained in their papers MR0435441 and MR0662439.

Fornaess and Stout proved that EVERY complex manifold (connected and second countable) can be covered by finitely many open subsets biholomorphic to a polydisc (Lemma II.1 in MR0470251). They even have an explicit bound on the size of the cover in terms of the dimension of the manifold. Further results of a similar flavour are contained in their papers MR0435441 and MR0662439.

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Finnur Larusson
Finnur Larusson
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Fornaess and Stout proved that EVERY complex manifold (connected and second countable) can be covered by finitely many relatively compact open subsets biholomorphic to a polydisc (Lemma II.1 in MR0470251). They even have an explicit bound on the size of the cover in terms of the dimension of the manifold. Further results of a similar flavour are contained in their papers MR0435441 and MR0662439.