摘要翻译：
给出了将S的开子集U上的光滑曲线族推广为S上的稳定曲线族的充分必要条件。更准确地说，我们引入了abelian monodromy扩张(AME)性质，证明了标准Deligne-Mumford紧性是曲线模空间唯一的极大AME紧性。我们还证明了Baily-Borel紧性是Abel簇模空间唯一的、最大射影AME紧性。
---
英文标题：
《The Abelian Monodromy Extension Property for Families of Curves》
---
作者：
Sabin Cautis
---
最新提交年份：
2008
---
分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--

---
英文摘要：
  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.
---
PDF链接：
https://arxiv.org/pdf/0709.3320