摘要翻译：
给定二维局部正则环R的一个双正规扩张S，我们描述了R中完全理想J的所有等性类型，它的爆破点使局部环解析同构。Spivakovsky(Ann.of Math.1990)已经提出了这种正规曲面奇点芽的分类问题。该问题分为离散和连续两部分。连续部分在一定程度上等价于平面曲线奇点的模问题，而本文的主要结果完全解决了离散部分。
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英文标题：
《Equisingularity classes of birational projections of normal
  singularities to a plane》
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作者：
Maria Alberich-Carraminana and Jesus Fernandez-Sanchez
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最新提交年份：
2007
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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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一级分类：Mathematics        数学
二级分类：Commutative Algebra        交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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英文摘要：
  Given a birational normal extension S of a two-dimensional local regular ring R, we describe all the equisingularity types of the complete ideals J in R whose blowing-up has some point at which the local ring is analytically isomorphic to S.   The problem of classifying the germs of such normal surface singularities was already posed by Spivakovsky (Ann. of Math. 1990). This problem has two parts: discrete and continous. The continous part is to some extent equivalent to the problem of the moduli of plane curve singularities, while the main result of this paper solves completely the discrete part.
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PDF链接：
https://arxiv.org/pdf/0707.1387