Compactifications of C^n and the complex projective space
Thomas Peternell

TL;DR
This paper investigates the unique ways complex projective space can compactify complex Euclidean space with smooth hypersurfaces, providing complete results for even dimensions and partial insights for odd dimensions.
Contribution
It proves that for even dimensions, complex projective space is the only such compactification, extending understanding of complex geometric structures.
Findings
Unique compactification for even n
Partial results for odd n
Confirmed case for n ≡ 1 mod 4 by Ping Li
Abstract
We show that the complex projective space is the only projective manifold compactifying by a smooth connected hypersurface, provided is even. In the odd dimensional case we give some partial results. The case when mod has now been settled by Ping Li.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory
