奇异点的局部k- h代数的导数

IF 0.7 4区数学 Q2 MATHEMATICS

Rocky Mountain Journal of Mathematics Pub Date : 2023-02-01 DOI:10.1216/rmj.2023.53.65

Naveed Hussain, S. Yau, Huaiqing Zuo

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引用次数: 0

摘要

在我们之前的工作中，我们引入了一系列与孤立超曲面奇点(V, 0)相关的新的派生李代数Lk(V)。这些是奇点的新的解析不变量。在这篇文章中，我们一方面研究了L2(V)对于几个多项式孤立奇点，得到了λk(V)的公式(即Lk(V)的维数)对于三项式奇点。进一步证明了L2(V)的锐上估计猜想。这一部分是我们之前在[HYZ8]工作的延续。另一方面，我们提出了τk(V)和λk(V)的两个新猜想，并证明了这两个猜想适用于一大类奇点。

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DERIVATIONS OF LOCAL k-TH HESSIAN ALGEBRAS OF SINGULARITIES

In our previous work, we introduced a series of new derivation Lie algebras Lk(V ) associated to an isolated hypersurface singularity (V, 0). These are new analytic invariants of singularities. In this article, on the one hand, we investigate L2(V ) for fewnomial isolated singularities and obtain the formula of λk(V ) (i.e., the dimension of Lk(V )) for trinomial singularities. Furthermore, we prove the sharp upper estimate conjecture for the L2(V ). This part is a continuous work of our previous work in [HYZ8]. On the other hand, we proposed two new conjectures for the τk(V ) and λk(V ) and we prove these conjectures for a large class of singularities.

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来源期刊

Rocky Mountain Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

7.5 months

期刊介绍： Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles. The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics. In addition, the journal publishes specialized conference proceedings.