The Abelian Monodromy Extension Property for Families of Curves

Details The Abelian Monodromy Extension Property for Families of Curves The Abelian Monodromy Extension Property for Families of Curves

2007-09-20

arxiv.org/abs/0709.3320v2

Mathematics

Algebraic Geometry

24 pages, 3 figures

Scientific paper

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

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