ON THE CONNECTIVITY OF BRANCH LOCI OF MODULI SPACES

被引：21

作者：

Bartolini, Gabriel ^{[1
]}

Costa, Antonio F. ^{[2
]}

Izquierdo, Milagros ^{[1
]}

机构：

[1] Linkoping Univ, Inst Matemat, S-58183 Linkoping, Sweden

[2] UNED, Fac Ciencias, Dept Matemat Fundamentales, Madrid 28040, Spain

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2013年 / 38卷 / 01期

基金：

瑞典研究理事会;

关键词：

Branch locus; moduli space; equisymmetric stratification; automorphisms of Riemann surfaces; RIEMANN SURFACES; ISOLATED POINTS; CONNECTEDNESS; CURVES;

D O I：

10.5186/aasfm.2013.3820

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The moduli space M-g of compact Riemann surfaces of genus g has orbifold structure and the set of singular points of the orbifold is the branch locus B-g. In this article we show that B-g is connected for genera three, four, thirteen, seventeen, nineteen and fiftynine, and disconnected for any other genus. In order to prove this we use Fuchsian groups, automorphisms of order 5 and 7 of Riemann surfaces, and calculations with GAP for some small genera.

引用

页码：245 / 258

页数：14

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