k-th Milnor numbers and k-th Tjurina numbers of weighted homogeneous singularities

Hussain Naveed; Liu Zhiwen; Yau Stephen S. -T.Zuo Huaiqing

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k-th Milnor numbers and k-th Tjurina numbers of weighted homogeneous singularities

机译：第 k 个 Milnor 数和第 k 个 Tjurina 数的加权齐次奇点数

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摘要

Let (V, 0) subset of (C-n, 0) be a weighted homogeneous isolated hypersurface singularity. In this paper, we give explicit formulas of its k-th Milnor numbers and the k-th Tjurina numbers in terms of its weight type. Moreover, we propose a sharp lower bound conjecture for the k-th Tjurina numbers and verify this conjecture for binomial singularities. We also give a new characterization for the simple hypersurface singularities.

机译：设（V， 0）的子集（C-n， 0）是一个加权均匀孤立的超表面奇点。在本文中，我们给出了其第 k 个 Milnor 数和第 k 个 Tjurina 数的权重类型的显式公式。此外，我们提出了第k个Tjurina数的尖锐下界猜想，并验证了二项式奇点的猜想。我们还对简单的超表面奇点进行了新的表征。

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来源
《Geometriae Dedicata》 |2023年第2期|共35页
作者
Hussain Naveed; Liu Zhiwen; Yau Stephen S. -T.Zuo Huaiqing;
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作者单位

Tsinghua Univ;

Yanqi Lake Beijing Inst Math Sci & Applicat;

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原文格式 PDF
正文语种英语
中图分类几何、拓扑;
关键词
Moduli algebra; Isolated singularity; Weighted homogeneous; Derivation Lie algebra; ISOLATED HYPERSURFACE SINGULARITIES; LIE-ALGEBRAS; COMPLEX STRUCTURES; MODULI ALGEBRAS; DERIVATIONS; NONEXISTENCE; INVARIANT;

机译：模代数;孤立奇点;加权均质;推导李代数;孤立的超表面奇点;李代数;复杂结构;模代数;衍生品;不存在;不变量;

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k-th Milnor numbers and k-th Tjurina numbers of weighted homogeneous singularities

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