“Weakly” elliptic Gorenstein singularities of surfaces
“Weakly” elliptic Gorenstein singularities of surfaces
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曲面的“弱”椭圆 Gorenstein 奇点
DOI：
10.1007/s002220050327
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发表时间：
1998
影响因子：
3.1
通讯作者：
A. Némethi
中科院分区：
文献类型：
--
作者：
A. Némethi
本文的主要信息是，Gorenstein奇点，其（真实的）的链接是合理的同调球，Artin-Laufer程序可以继续。在这里，我们给出了完整的答案的情况下，椭圆奇点。本文的主要结果是，在椭圆Gorenstein奇点的情况下，其链接是合理的同调球，几何亏格是一个拓扑不变量。实际上，它正好是椭圆序列在最小分辨率下的长度（或者，等价地，在S中）。S.- T.丘的术语：这些奇点是最大椭圆的）。本文利用这一性质刻画了奇点，并从奇点的分解图中计算了奇点的Hilbert-Samuel函数（推广了Laufer和Yau的一些结果）。将法面奇点成为极大椭圆的障碍与某些Picard群的挠部分联系起来，这是本文的新思想。
The main message of the paper is that for Gorenstein singularities, whose (real) link is rational homology sphere, the Artin--Laufer program can be continued. Here we give the complete answer in the case of elliptic singularities. The main result of the paper says that in the case of an elliptic Gorenstein singularity whose link is rational homology sphere, the geometric genus is a topological invariant. Actually, it is exactly the length of the elliptic sequence in the minimal resolution (or, equivalently, in S. S.-T. Yau's terminology: these singularities are maximally elliptic). In the paper we characterize the singularities with this property, and we compute their Hilbert-Samuel function from their resolution graph (generalizing some results of Laufer and Yau). The obstruction for a normal surface singularity to be maximally elliptic can be connected with the torsion part of some Picard groups, this is the new idea of the paper.