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Uniqueness of equivariant compactifications of C^n by a Fano manifold of Picard number 1

Baohua FU AMSS, Chinese Academy of Sciences Jun-Muk Hwang KIAS

mathscidoc:1702.01006

Distinguished Paper Award in 2017

Math. Res. Lett., 2014
Let X be an n -dimensional Fano manifold of Picard number 1. We study how many different ways X can compactify the complex vector group C^n equivariantly. Hassett and Tschinkel showed that when X = P^n with n \geq 2, there are many distinct ways that X can be realized as equivariant compactifications of C^n. Our result says that projective space is an exception: among Fano manifolds of Picard number 1 with smooth VMRT, projective space is the only one compactifying C^n equivariantly in more than one ways. This answers questions raised by Hassett-Tschinkel and Arzhantsev-Sharoyko.
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@inproceedings{baohua2014uniqueness,
  title={Uniqueness of equivariant compactifications of C^n by a Fano manifold of Picard number 1},
  author={Baohua FU, and Jun-Muk Hwang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170210114709597001425},
  booktitle={Math. Res. Lett.},
  year={2014},
}
Baohua FU, and Jun-Muk Hwang. Uniqueness of equivariant compactifications of C^n by a Fano manifold of Picard number 1. 2014. In Math. Res. Lett.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170210114709597001425.
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