标题： 通过谱数表征孤立超曲面奇点的特殊矩阵 显示英文标题

标题： Characterization of distinguished matrices of isolated hypersurface singularities through their spectral numbers

摘要： 孤立超曲面奇点配备了其Milnor格的特殊基和上三角整数矩阵，这些矩阵在此被称为特殊矩阵。 这些矩阵构成了一个辫群和符号变化群的轨道。 本文提出通过某些谱数的方差来表征奇点的特殊矩阵，在所有上三角整数矩阵中进行表征。 它在正定和半正定情况下取得了成功。 ADE根格是关键。 在半定情况下，使用了关于Weyl群元素的非约化表示的结果。 显示英文摘要

摘要： Isolated hypersurface singularities come equipped with distinguished bases of their Milnor lattices and with upper triangular integral matrices, which are called here distinguished matrices. These matrices form an orbit of a braid group and a sign change group. This paper proposes to characterize the distinguished matrices of singularities within all upper triangular integral matrices in terms of the variance of certain spectral numbers. It succeeds in the positive definite and the positive semidefinite cases. The ADE root lattices are crucial. In the semidefinite cases, results on non-reduced presentations of Weyl group elements are used.