The structures of hypersurface simple K3 singularities

我们证明了由非拟齐次多项式定义的非简并简单K3奇点的无穷多链路的存在性，而在由拟齐次多项式定义的奇点中不存在无穷多链路。此外，我们还给出了非简并半拟齐次超曲面简单K3奇点的链路的微分同态类型与作为奇点分辨率的例外除数的正规K3曲面的奇点之间的关系。在某些条件下，我们还将一些复杂三维超曲面孤立奇点的链路划分为正则同伦。

We show the existence of infinitely many links of non-degenerate simple K3 singularities defined by non-quasi-homogeneous polynomials, which do not appear in the case of the singularities defined by quasi-homogeneous polynomials. Moreover, we give a result that relates the diffeomorphism types of the links of non-degenerate semi-quasi-homogeneous hypersurface simple K3 singularities with the singularities of the normal K3 surface that appears as the exceptional divisor of the resolution of the singularity. We also classify links of the some complex 3-dimensional hypersurface isolated singularities up to regular homotopies under some conditions.