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We study the Milnor monodromies of non-isolated hypersurface singularitiesand show that the reduced cohomology groups of the Milnor fibers areconcentrated in the middle degree for some eigenvalues of the monodromies. Asan application of this result, we give an explicit formula for some parts oftheir Jordan normal forms.

Milnor monodromies and mixed Hodge structures for non-isolated hypersurface singularities