On the compactification of strongly pseudoconvex surfaces. II

Tan, Vo Van

doi:10.1090/S0002-9939-1984-0727230-4

On the compactification of strongly pseudoconvex surfaces. II
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Proc. Amer. Math. Soc. 90 (1984), 189-194 Request permission

Abstract:

A complete answer to the following question is given: When is an algebraic surface $M$ a compactification of some strongly pseudoconvex surface? In particular, we show this will not be the case if $M$ is either ${{\mathbf {P}}_2}$, a quadric, an abelian surface, or a hyperelliptic surface. On the other hand, by constructing specific examples, we show that this will be the case for all other algebraic surfaces. Furthermore, we prove that any compactifiable strongly pseudoconvex surface is quasi-projective.

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