Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE FINITENESS OF REAL STRUCTURES OF PROJECTIVE MANIFOLDS

  • Kim, Jin Hong (Department of Mathematics Education Chosun University)
  • Received : 2019.01.24
  • Accepted : 2019.03.04
  • Published : 2020.01.31
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Abstract

Recently, Lesieutre constructed a 6-dimensional projective variety X over any field of characteristic zero whose automorphism group Aut(X) is discrete but not finitely generated. As an application, he also showed that X is an example of a projective variety with infinitely many non-isomorphic real structures. On the other hand, there are also several finiteness results of real structures of projective varieties. The aim of this short paper is to give a sufficient condition for the finiteness of real structures on a projective manifold in terms of the structure of the automorphism group. To be more precise, in this paper we show that, when X is a projective manifold of any dimension≥ 2, if Aut(X) does not contain a subgroup isomorphic to the non-abelian free group ℤ ∗ ℤ, then there are only finitely many real structures on X, up to ℝ-isomorphisms.

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References

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