摘要翻译：
我们证明了“端曲线定理”，它指出具有有理同调球环的法面奇点$(X，o)$是拼接商奇点当且仅当它对一棵高分辨率树的每一片叶子都有一个端曲线函数。“端曲线函数”是一个解析函数$(X，o)\to(\c，0)$，它的零点集与$\sigma$在对应于给定叶子的异常曲线的子午线曲线给出的结中相交。通过给出一组显式的方程组来描述一个“剪接商奇点”$(X,o)$,其中$t$是$(X,o)$分解图中的叶数，并给出了覆盖变换群的显式描述，该方程组将其泛阿贝尔覆盖描述为$\c^t$中的完全交集。在端曲线定理的直接结果中，有先前已知的结果:$(X，o)$是一个拼接商，如果它是加权齐次的(Neumann1981)，或者有理的或最小椭圆的(Okuma2005)。
---
英文标题：
《The End Curve Theorem for normal complex surface singularities》
---
作者：
Walter D Neumann and Jonathan Wahl
---
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
--
一级分类：Mathematics        数学
二级分类：Geometric Topology        几何拓扑
分类描述：Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形，轨道，多面体，细胞复合体，叶状，几何结构
--

---
英文摘要：
  We prove the "End Curve Theorem," which states that a normal surface singularity $(X,o)$ with rational homology sphere link $\Sigma$ is a splice-quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree.   An "end-curve function" is an analytic function $(X,o)\to (\C,0)$ whose zero set intersects $\Sigma$ in the knot given by a meridian curve of the exceptional curve corresponding to the given leaf.   A "splice-quotient singularity" $(X,o)$ is described by giving an explicit set of equations describing its universal abelian cover as a complete intersection in $\C^t$, where $t$ is the number of leaves in the resolution graph for $(X,o)$, together with an explicit description of the covering transformation group.   Among the immediate consequences of the End Curve Theorem are the previously known results: $(X,o)$ is a splice quotient if it is weighted homogeneous (Neumann 1981), or rational or minimally elliptic (Okuma 2005).
---
PDF链接：
https://arxiv.org/pdf/0804.4644