Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness of equivariant compactifications of C^n by a Fano manifold of
  Picard number 1   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.

9
The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th