2017
DOI: 10.1090/tran/6988
|View full text |Cite
|
Sign up to set email alerts
|

Families of Riemann surfaces, uniformization and arithmeticity

Abstract: A consequence of the results of Bers and Griffiths on the uniformization of complex algebraic varieties is that the universal cover of a family of Riemann surfaces, with base and fibers of finite hyperbolic type, is a contractible 2 − 2- dimensional domain that can be realized as the graph of a holomorphic motion of the unit disk. In this paper we determine which holomorphic motions give rise to these uniformizing domains and characterize which among them correspond to arith… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
5

Citation Types

0
8
0

Year Published

2019
2019
2021
2021

Publication Types

Select...
5
1

Relationship

2
4

Authors

Journals

citations
Cited by 9 publications
(9 citation statements)
references
References 25 publications
0
8
0
Order By: Relevance
“…As pointed out in [12] and [13], we remark that, in this respect, complex surfaces are very much in contrast with compact Riemann surfaces, for which the universal cover only depends on the genus.…”
Section: Introduction and Statement Of Resultsmentioning
confidence: 56%
See 2 more Smart Citations
“…As pointed out in [12] and [13], we remark that, in this respect, complex surfaces are very much in contrast with compact Riemann surfaces, for which the universal cover only depends on the genus.…”
Section: Introduction and Statement Of Resultsmentioning
confidence: 56%
“…Let S be a non-singular minimal projective surface of general type. Based on results due to Bers and Griffiths [3,14] on uniformization of complex projective varieties and on results of Shabat [18,19] on automorphism groups of universal covers of families of Riemann surfaces, in [13] the authors succeeded in proving that whether or not S is defined over a given algebraically closed field depends only on the holomorphic universal cover of its Zariski open subsets.…”
Section: Introduction and Statement Of Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…(2) A theorem of Griffiths [15] implies that there exist examples of domains Ω ⊂ C 2 where Aut(Ω) is infinite, discrete and the quotient Aut(Ω)\Ω is compact (see [13] for details). The last condition implies that L(Ω) = ∂Ω.…”
Section: Introductionmentioning
confidence: 99%
“…In the less general case of pseudoconvex domains with real analytic boundary, Catlin's results are not needed and instead one could use results of Kohn [Koh77] and Diederich and Fornaess [DF78]. (3) A theorem of Griffiths [Gri71] implies that there exists examples of domains Ω ⊂ C 2 where Aut(Ω) is infinite, discrete, and the quotient Aut(Ω)\Ω is compact (see [GR15] for details). The last condition implies that L(Ω) = ∂Ω.…”
Section: Introductionmentioning
confidence: 99%