On the connectedness of the branch loci of moduli spaces of orientable Klein surfaces

被引：0
作者：
Antonio F. Costa
Milagros Izquierdo
Ana M. Porto
机构：
[1] UNED,Departamento de Matematicas
[2] Linköpings Universitet,Matematiska institutionen
来源：
Geometriae Dedicata | 2015年 / 177卷
关键词：
Klein surface; Riemann surface; Moduli space; Automorphism; 30F50; 30F10; 14H37;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let M(g,+,k)K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {M}_{(g,+,k)}^{K}$$\end{document} be the moduli space of orientable Klein surfaces of genus g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g$$\end{document} with k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document} boundary components (see Alling and Greenleaf in Lecture notes in mathematics, vol 219. Springer, Berlin, 1971; Natanzon in Russ Math Surv 45(6):53–108, 1990). The space M(g,+,k)K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {M}_{(g,+,k)} ^{K}$$\end{document} has a natural orbifold structure with singular locus B(g,+,k)K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {B} _{(g,+,k)}^{K}$$\end{document}. If g>2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g>2$$\end{document} or k>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k>0$$\end{document} and 2g+k>3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2g+k>3$$\end{document} the set B(g,+,k)K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {B} _{(g,+,k)}^{K}$$\end{document} consists of the Klein surfaces admitting non-trivial symmetries and we prove that, in this case, the singular locus is connected.
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页码：149 / 164
页数：15
相关论文
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