## Tokyo Journal of Mathematics

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

Masahide KATO

#### 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

https://projecteuclid.org/euclid.tjm/1313074454

Digital Object Identifier
doi:10.3836/tjm/1313074454

Mathematical Reviews number (MathSciNet)
MR2866646

Zentralblatt MATH identifier
1238.32015

#### 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

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