PreprintCC BY 4.0arXiv
Projective compactifications of hypersurface complements
Abstract
Let U be a smooth affine variety of the form U=Pn∖ H, where H⊂Pn is a smooth connected hypersurface. We prove that every smooth projective compactification of the complex manifold U, by adding a smooth connected divisor, is isomorphic to Pn. The proof uses the rational Reeb index of the normal circle bundle and positive S1-equivariant symplectic homology. This paper is motivated by the work of Chi Li and Zhengyi Zhou, and makes a generalization to their result.
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BibTeX
@misc{wang2026projective,
title = {{Projective compactifications of hypersurface complements}},
author = {Hairun Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38376},
eprint = {2610.38376},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38376},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Projective compactifications of hypersurface complements
AU - Hairun Wang
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38376
UR - https://arxiv.org/abs/2610.38376
AB - Let U be a smooth affine variety of the form U=P^n∖ H, where H⊂P^n is a smooth connected hypersurface. We prove that every smooth projective compactification of the complex manifold U, by adding a smooth connected divisor, is isomorphic to P^n. The proof uses the rational Reeb index of the normal circle bundle and positive S^1-equivariant symplectic homology. This paper is motivated by the work of Chi Li and Zhengyi Zhou, and makes a generalization to their result.
ER -