The integral monodromy on the Milnor lattice of an isolated quasihomogeneous singularity is subject of an almost untouched conjecture of Orlik from 1972. We prove this conjecture for all iterated Thom–Sebastiani sums of chain type singularities and cycle type singularities. The main part of the paper is purely algebraic. It provides tools for dealing with sums and tensor products of $\mathbb{Z}$-lattices with automorphisms of finite order and with cyclic generators. The calculations are involved. They use fine properties of unit roots, cyclotomic polynomials, their resultants and discriminants.

中文翻译：

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孤立准齐次奇点的积分单调

孤立的准齐次奇点的 Milnor 晶格上的积分单调是 Orlik 自 1972 年以来几乎未触及的猜想的主题。我们为链型奇点和环型奇点的所有迭代 Thom-Sebastiani 和证明了这一猜想。论文的主要部分是纯代数的。它提供了处理总和和张量积的工具$\mathbb{Z}$-具有有限阶自同构和循环生成器的格。涉及计算。他们使用单位根、分圆多项式、它们的结果和判别式的精细性质。