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Geometric Monodromies, Mixed Hodge Numbers of Motivic Milnor Fibers and Newton Polyhedra

In: Handbook of Geometry and Topology of Singularities VII

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  • Kiyoshi Takeuchi

    (Tohoku University, Mathematical Institute)

Abstract

We introduce the theory of local and global monodromies of polynomials in cohomology groups in various geometric situations, focusing on its relations with toric geometry and motivic Milnor fibers, and moreover in the modern languages of nearby and vanishing cycle functors. Equivariant mixed Hodge numbers of motivic Milnor fibers will be described in terms of Newton polyhedra of polynomials.

Suggested Citation

  • Kiyoshi Takeuchi, 2025. "Geometric Monodromies, Mixed Hodge Numbers of Motivic Milnor Fibers and Newton Polyhedra," Springer Books, in: José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities VII, chapter 0, pages 643-720, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-68711-2_12
    DOI: 10.1007/978-3-031-68711-2_12
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