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

Baohua Fu; Jun-Muk Hwang

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arXiv · 1301.5486

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

Baohua Fu·Jun-Muk Hwang

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Abstract

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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Baohua Fu, Jun-Muk Hwang. 2013-01-23. Uniqueness of equivariant compactifications of C^n by a Fano manifold of Picard number 1. https://arxiv.org/abs/1301.5486

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