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Proceedings of the American Mathematical Society

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



On the compactification of strongly pseudoconvex surfaces. II

Author: Vo Van Tan
Journal: Proc. Amer. Math. Soc. 90 (1984), 189-194
MSC: Primary 32J05; Secondary 32F30
MathSciNet review: 727230
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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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Keywords: Classification of algebraic surfaces, canonical dimension, compactifiable strongly pseudoconvex surfaces, quasi-projective structure, affine $ C$-bundle over elliptic curve
Article copyright: © Copyright 1984 American Mathematical Society