摘要翻译：
推广了Deligne-Mumford和de Jong关于真曲线族半稳定修正的定理。主要结果表明，在基部发生一般变化后，任何具有半稳定一般纤维的多点曲线族（不一定是适当的）都允许一个最小的半稳定变化。后者还可以用它的几何纤维没有某些特殊成分的性质来表征。我们证明的主要步骤是值域的一维扩张的一致化。然后利用Riemann-Zariski空间得到任意积分基上的结果。
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英文标题：
《Stable modification of relative curves》
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作者：
Michael Temkin
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最新提交年份：
2010
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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
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英文摘要：
  We generalize theorems of Deligne-Mumford and de Jong on semi-stable modifications of families of proper curves. The main result states that after a generically \'etale alteration of the base any (not necessarily proper) family of multipointed curves with semi-stable generic fiber admits a minimal semi-stable modification. The latter can also be characterized by the property that its geometric fibers have no certain exceptional components. The main step of our proof is uniformization of one-dimensional extensions of valued fields. Riemann-Zariski spaces are then used to obtain the result over any integral base.
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PDF链接：
https://arxiv.org/pdf/0707.3953