Mixed Hodge Structures Applied to Singularities

Joseph Steenbrink ()
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Joseph Steenbrink: Radboud University Nijmegen, IMAPP

Chapter Chapter 9 in Handbook of Geometry and Topology of Singularities III, 2022, pp 645-678 from Springer

Abstract: 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-95760-5_9

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DOI: 10.1007/978-3-030-95760-5_9

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