A study of complex surface singularities whose link is a rational homology sphere

研究了复法向曲面奇异性的基本解析不变量，如几何格。对于具有理性同调球连杆的加权齐次奇点，我们利用Seifert不变量（与a . Nemethi联合工作）表示了切轴在最小良好分辨率上的第一上同调群的维数。我们引入了pg-环的概念并研究了基本性质，然后对Gorenstein奇点和有理奇点证明了好理想的存在，并进一步证明了有理奇点的好理想对应于最小分辨率上的网络环（与Kei-ichi Watanabe和Ken-ichi Yoshida合作）。并给出了Brieskorn型完全交点上最大理想环的一个显式表达式（与Fan-Ning孟联合工作）。这推广了Konno和Nagashima关于Brieskorn超曲面的结果。

We studied fundamental analytic invariants of complex normal surface singularities, such as geometric genus. For a weighted homogeneous singularity with rational homology sphere link, we expressed the dimension of the first cohomology group of the tangent sheaf on the minimal good resolution using Seifert invariants (joint work with A. Nemethi). We introduced a notion of pg-cycle and investigated fundamental properties, and then for Gorenstein singularities and rational singularities, we proved that the good ideal exists, and furthermore that good ideals for rational singularities correspond to nef cycles on the minimal resolution (joint work with Kei-ichi Watanabe and Ken-ichi Yoshida). We also gave an explicit expression of the maximal ideal cycle on a complete intersection of Brieskorn type (joint work with Fan-Ning Meng). This generalizes the results by Konno and Nagashima for Brieskorn hypersurfaces.