Mathematische Annalen

, Volume 344, Issue 3, pp 717–747

The abelian monodromy extension property for families of curves

Article

DOI: 10.1007/s00208-008-0324-2

Cite this article as:
Cautis, S. Math. Ann. (2009) 344: 717. doi:10.1007/s00208-008-0324-2

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.

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsRice UniversityHoustonUSA

Personalised recommendations