Perverse Leray filtration and specialisation with applications to the Hitchin morphism

We initiate and develop a framework to handle the specialisation morphism as a filtered morphism for the perverse, and for the perverse Leray filtration, on the cohomology with constructible coefficients of varieties and morphisms parameterised by a curve. As an application, we use this framework to...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2022-03, Vol.172 (2), p.443-487
Main Author: DE CATALDO, MARK ANDREA A.
Format: Article
Language:English
Subjects:
Filtration
Homology
Specialization
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Summary:We initiate and develop a framework to handle the specialisation morphism as a filtered morphism for the perverse, and for the perverse Leray filtration, on the cohomology with constructible coefficients of varieties and morphisms parameterised by a curve. As an application, we use this framework to carry out a detailed study of filtered specialisation for the Hitchin morphisms associated with the compactification of Dolbeault moduli spaces in [de 2018].
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004121000293