The abelian monodromy extension property for families of curves

被引：0
作者：
Sabin Cautis
机构：
[1] Rice University,Department of Mathematics
来源：
Mathematische Annalen | 2009年 / 344卷
关键词：
Modulus Space; Abelian Variety; Exceptional Divisor; Mapping Class Group; Dehn Twist;
D O I：
暂无
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学科分类号：
摘要：
Necessary and sufficient conditions are given (in terms of monodromy) for extending a family of smooth curves over an open subset \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${U \subset S}$$\end{document} to a family of stable curves over S. More precisely, we introduce the abelian monodromy extension (AME) property and show that the standard Deligne–Mumford compactification is the unique, maximal AME compactification of the moduli space of curves. We also show that the Baily–Borel compactification is the unique, maximal projective AME compactification of the moduli space of abelian varieties.
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页码：717 / 747
页数：30
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