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2017•arXiv (Cornell University)Open access

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

Takahiro Saito

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Abstract

We study the Milnor monodromies of non-isolated hypersurface singularities and show that the reduced cohomology groups of the Milnor fibers are concentrated in the middle degree for some eigenvalues of the monodromies. As an application of this result, we give an explicit formula for some parts of their Jordan normal forms.

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We study the Milnor monodromies of non-isolated hypersurface singularities and show that the reduced cohomology groups of the Milnor fibers are concentrated in the middle degree for some eigenvalues of the monodromies. As an application of this result, we give an explicit formula for some parts of their Jordan normal forms.

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Available abstract

We study the Milnor monodromies of non-isolated hypersurface singularities and show that the reduced cohomology groups of the Milnor fibers are concentrated in the middle degree for some eigenvalues of the monodromies. As an application of this result, we give an explicit formula for some parts of their Jordan normal forms.

Key concepts: Hypersurface, Gravitational singularity, Mathematics, Pure mathematics, Cohomology, Eigenvalues and eigenvectors, Hodge theory, Mathematical analysis

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