On superheight conditions for the affineness of open subsets

Mathematics – Commutative Algebra

Scientific paper

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20 pages

Scientific paper

In this paper we consider the open complement U of a hypersurface Y=V(a) in
an affine scheme X. We study the relations between the affineness of U, the
intersection of Y with closed subschemes, the property that every closed
surface in U is affine, the property that every analytic closed surface is
Stein and the superheight of the defining ideal a.

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