Tokyo Journal of Mathematics

Existence of Invariant Planes in a Complex Projective 3-Space under Discrete Projective Transformation Groups

Masahide KATO

Full-text: Open access

Abstract

Let $\Gamma$ be a finitely generated discrete subgroup of $\mathrm{PGL}(4,\mathbf{C})$ acting on $\mathbf{P}^3$. Suppose that $\Gamma$ leaves invariant a surface in $\mathbf{P}^3$. Then, except for a few cases, we can find a plane which is invariant by a finite index subgroup of $\Gamma$. The exceptional cases will be determined explicitly.

Article information

Source
Tokyo J. Math., Volume 34, Number 1 (2011), 261-285.

Dates
First available in Project Euclid: 11 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1313074454

Digital Object Identifier
doi:10.3836/tjm/1313074454

Mathematical Reviews number (MathSciNet)
MR2866646

Zentralblatt MATH identifier
1238.32015

Subjects
Primary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]
Secondary: 32J17: Compact $3$-folds 14J50: Automorphisms of surfaces and higher-dimensional varieties

Citation

KATO, Masahide. Existence of Invariant Planes in a Complex Projective 3-Space under Discrete Projective Transformation Groups. Tokyo J. Math. 34 (2011), no. 1, 261--285. doi:10.3836/tjm/1313074454. https://projecteuclid.org/euclid.tjm/1313074454


Export citation

References

  • Bers, L., Inequalities for finitely generated Kleinian groups, J. d'Analyse Math., 18 (1967), 23–41.
  • Griffiths, P. and Harris, J., Principles of Algebraic Geometry, A Wiley-Interscience Publication, John Wiley & Sons, Inc., 1978.
  • Kato, Ma., On compact complex 3-folds with lines, Japanese J. Math., 11 (1985), 1–58.
  • Kato, Ma., Compact quotients with positive algebraic dimensions of large domains in a complex projective 3-space, J. Math. Soc. of Japan, 62 (2010), 1317–1371.
  • Matsuzaki, K. and Taniguchi, M., Hyperbolic Manifolds and Kleinian Groups, Oxford Math. Mono., Oxford Sci. Publ., 1998.