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On the rigidity of certain discrete groups and algebraic varieties

J Jost Shing-Tung Yau

Algebraic Geometry mathscidoc:1912.43572

Mathematische Annalen, 278, (1), 481-496, 1987.3
Theorem 1. Let D be an irreducible bounded symmetric domain in C', n>= 2. Let F be a (nonuniform) lattice in Aut (D), ie a discrete subgroup of Aut (D) for which N:= D/F (is noncompact and) has. finite volume (wrt the locally symmetric metric induced from D). Suppose that a group F isomorphic to F (as an abstract group) acts as a discrete automorphism group on a contractible K (ihler manifold tVI. Assume that lQ/f has a finite singularity free cover M (ie M is a manifold) which is quasiprojective ie admits a compactification as a projective variety IVI and that~ I\M is of codimension at least three in~ l. Then] Q is biholomorphically equivalent to D, and f is conjugate to F in Aut (D).
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@inproceedings{j1987on,
  title={On the rigidity of certain discrete groups and algebraic varieties},
  author={J Jost, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204126353415136},
  booktitle={Mathematische Annalen},
  volume={278},
  number={1},
  pages={481-496},
  year={1987},
}
J Jost, and Shing-Tung Yau. On the rigidity of certain discrete groups and algebraic varieties. 1987. Vol. 278. In Mathematische Annalen. pp.481-496. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204126353415136.
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