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Mathematische Annalen

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

The abelian monodromy extension property for families of curves

  • Sabin CautisEmail author
Article

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsRice UniversityHoustonUSA

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