Mirror stabilizers for lattice complex hyperbolic triangle groups

被引：0
作者：
Deraux, Martin [1 ,2 ,3 ]
机构：
[1] Univ Grenoble Alpes, CNRS, IF, F-38000 Grenoble, France
[2] Sorbonne Univ, Paris, France
[3] Univ Paris, Ouragan, CNRS, INRIA,IMJ PRG, F-75005 Paris, France
来源：
GEOMETRIAE DEDICATA | 2024年 / 218卷 / 03期
关键词：
Complex hyperbolic geometry; Lattices; Totally geodesic submanifolds; SUBGROUPS;
D O I：
10.1007/s10711-024-00910-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For each lattice complex hyperbolic triangle group, we study the Fuchsian stabilizers of (reprentatives of each group orbit of) mirrors of complex reflections. We give explicit generators for the stabilizers, and compute their signature in the sense of Fuchsian groups. For some groups, we also find explicit pairs of complex lines such that the union of their stabilizers generate the ambient lattice.
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页数：29
相关论文
共 23 条
  • [1] Barthel Gottfried., 1987, Geradenkonfigurationen und Algebraische Flachen
  • [2] Beardon A. F., 1983, GEOMETRY DISCRETE GR, V91, DOI [10.1007/978-1-4612-1146-4, DOI 10.1007/978-1-4612-1146-4]
  • [3] ARITHMETIC SUBGROUPS OF ALGEBRAIC GROUPS
    BOREL, A
    HARISHCHANDRA
    [J]. ANNALS OF MATHEMATICS, 1962, 75 (03) : 485 - &
  • [4] Chen S., 1974, Contributions to Analysis, P49
  • [5] Geometric structures on the complement of a projective arrangement
    Couwenberg, W
    Heckman, G
    Looijenga, E
    [J]. PUBLICATIONS MATHEMATIQUES DE L'IHES, NO 101, 2005, 101 (101): : 69 - 161
  • [6] de Rham G., 1971, Enseign. Math, V2, P49
  • [7] DELIGNE P, 1986, PUBL MATH-PARIS, P5
  • [8] Deraux M., 2019, SPOCHECK
  • [9] Deraux M., GITLAB PROJECT NEAT
  • [10] New Nonarithmetic Complex Hyperbolic Lattices II
    Deraux, Martin
    Parker, John R.
    Paupert, Julien
    [J]. MICHIGAN MATHEMATICAL JOURNAL, 2021, 70 (01) : 133 - 205
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