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Mixed Hodge Structures Applied to Singularities

In: Handbook of Geometry and Topology of Singularities III

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  • Joseph Steenbrink

    (Radboud University Nijmegen, IMAPP)

Abstract

We give a survey of applications of mixed Hodge theory to the study of isolated singularities. A summary of mixed Hodge theory is followed by some examples. The formalism of vanishing cycles is realized on the Hodge level by a sheaf complex with three filtrations, making the application to the cohomology of the Milnor fibre possible. The approaches by algebraic analysis and by motivic integration are discussed, and the spectrum with its properties is considered. The paper ends with a treatment of Du Bois singularities.

Suggested Citation

  • Joseph Steenbrink, 2022. "Mixed Hodge Structures Applied to Singularities," Springer Books, in: José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities III, chapter 0, pages 645-678, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-95760-5_9
    DOI: 10.1007/978-3-030-95760-5_9
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