Abstract
This paper discusses some recent progress on Schottky group actions on compact and non-compact complex manifolds.
Dedicated to Kang-Tae Kim at the occasion of his 60th birthday.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A flag manifold \(X=G/P\) is called irreducible if P is a maximal parabolic subgroup of G, i.e., if P is not properly contained in any proper parabolic subgroup of G.
References
Akhiezer, D.N.: Dense orbits with two endpoints. Izv. Akad. Nauk SSSR Ser. Mat. 41(2), 308–324 (1977). 477
Blanchard, A.: Sur les variétés analytiques complexes. Ann. Sci. Ecole Norm. Sup. 73, 157–202 (1956)
Bowditch, B.H.: Geometrical finiteness with variable negative curvature. Duke Math. J. 77(1), 229–274 (1995)
Bremigan, R., Lorch, J.: Orbit duality for flag manifolds. Manuscripta Math. 109(2), 233–261 (2002)
Cano, A.: Schottky groups can not act on \(\mathbf{P}^{2n}_{\mathbf{C}}\) as subgroups of \({\rm PSL}_{2n+1} (\mathbf{C})\). Bull. Braz. Math. Soc. (N.S.) 39(4), 573–586 (2008)
Cano, A., Navarrete, J.P., Seade, J.: Complex Kleinian Groups, Progress in Mathematics, vol. 303. Birkhäuser/Springer Basel AG, Basel (2013)
Goldman, W.M.: Complex hyperbolic geometry. Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1999)
Guillot, A.: Sur les équations d’Halphen et les actions de \({\rm SL}_2(\mathbb{C})\). Publ. Math. Inst. Hautes Études Sci. 105, 221–294 (2007)
Kapovich, M., Leeb, B., Porti, J.: Some recent results on Anosov representations. Transform. Groups 21(4), 1105–1121 (2016)
Kato, M.: Examples of simply connected compact complex 3-folds. Tokyo J. Math. 5(2), 341–264 (1982)
Kato, M.: On compact complex \(3\)-folds with lines. Tokyo J. Math. 11 (1985)
Kato, M.: Factorization of compact complex \(3\)-folds which admit certain projective structures. Tôhoku Math. J. 41, 359–397 (1989)
Kato, M.: Compact quotients with positive algebraic dimensions of large domains in a complex projective 3-space. J. Math. Soc. Jpn 62(4), 1317–1371 (2010)
Koebe, P.: Über die Uniformisierung der algebraischen Kurven II. Math. Ann. 69(1), 1–81 (1910)
Lárusson, F.: Compact quotients of large domains in complex projective space. Ann. Inst. Fourier (Grenoble) 48(1), 223–246 (1998)
Link, G.: Geometry and dynamics of discrete isometry groups of higher rank symmetric spaces. Geom. Dedicata 122, 51–75 (2006)
Maskit, B.: A characterization of Schottky groups. J. Analyse Math. 19, 227–230 (1967)
Miebach, C., Oeljeklaus, K.: Schottky groups acting on homogeneous rational manifolds. J. Reine Angew. Math. https://doi.org/10.1515/crelle-2016-0065 (to appear)
Nori, M.V.: Schottky, The groups in higher dimensions, The Lefschetz centennial conference, Part I (Mexico City, Contemp. Math., vol. 58, Amer. Math. Soc. Providence, RI 1986, 195–197 (1984)
Seade, J., Verjovsky, A.: Complex Schottky groups. Astérisque 287(xx), 251–272 (2003). Geometric methods in dynamics. II
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Miebach, C., Oeljeklaus, K. (2018). Schottky Group Actions in Complex Geometry. In: Byun, J., Cho, H., Kim, S., Lee, KH., Park, JD. (eds) Geometric Complex Analysis. Springer Proceedings in Mathematics & Statistics, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-13-1672-2_20
Download citation
DOI: https://doi.org/10.1007/978-981-13-1672-2_20
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-1671-5
Online ISBN: 978-981-13-1672-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)