## Tokyo Journal of Mathematics

### Compact Quotients of Large Domains in a Complex Projective 3-space

Masahide Kato

#### Abstract

In a complex projective 3-space, we consider a domain with a projective line. If there is a compact non-singular quotient of the domain and the quotient manifold admits a non-constant meromorphic function, then the domain is dense in the projective 3-space and its complement is properly contained in a finite union of complex hypersurfaces and a set with Hausdorff dimension not more than two. Further, if the complement admits a certain fiber space structure, then it is either a disjoint union of two projective lines, a projective line, or an empty set.

#### Article information

Source
Tokyo J. Math., Volume 29, Number 1 (2006), 209-232.

Dates
First available in Project Euclid: 20 December 2006

https://projecteuclid.org/euclid.tjm/1166661875

Digital Object Identifier
doi:10.3836/tjm/1166661875

Mathematical Reviews number (MathSciNet)
MR2258280

Zentralblatt MATH identifier
1116.32011

Subjects
Primary: 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions
Secondary: 32J17: Compact $3$-folds

#### Citation

Kato, Masahide. Compact Quotients of Large Domains in a Complex Projective 3-space. Tokyo J. Math. 29 (2006), no. 1, 209--232. doi:10.3836/tjm/1166661875. https://projecteuclid.org/euclid.tjm/1166661875

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