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Eigenvalues for the monodromy of the Milnor fibers of arrangements. (English) Zbl 1036.32019
Libgober, Anatoly (ed.) et al., Trends in singularities. Basel: Birkhäuser (ISBN 3-7643-6704-0/hbk). Trends in Mathematics, 141-150 (2002).
Let $$l_1,\dots, l_d$$ be $$d$$ linear forms on $$\mathbb{C}^{n+1}$$, $$A$$ the cone of the equation $$\prod l_i= 0$$ and $${\mathcal A}$$ the corresponding arrangement of hyperplanes in $$\mathbb{P}^n$$. If $$F_A$$ is the Milnor fiber of $$A$$ at $$0$$, the author describes, in terms of the combinatorics of $${\mathcal A}$$, upper bounds for the orders of the eigenvalues of the monodromy acting on $$H_k(F_A, \mathbb{C})$$ $$(k\leq n-1)$$. When $$n= 2$$ he also computes the multiplicities of these eigenvalues. He then studies several examples giving in particular some conditions implying that eigenvalues different from 1 can only occur in top dimension.
For the entire collection see [Zbl 0997.00011].

##### MSC:
 32S22 Relations with arrangements of hyperplanes 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects)