Mathematische Annalen

, Volume 344, Issue 3, pp 717–747 | Cite as

The abelian monodromy extension property for families of curves

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Abstract

Necessary and sufficient conditions are given (in terms of monodromy) for extending a family of smooth curves over an open subset \({U \subset S}\) 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.

Keywords

Modulus Space Abelian Variety Exceptional Divisor Mapping Class Group Dehn Twist 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsRice UniversityHoustonUSA

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