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Perverse Leray filtration and specialisation with applications to the Hitchin morphism

Part of: Families, fibrations Curves Algebraic geometry: Foundations

Published online by Cambridge University Press:  20 April 2021

MARK ANDREA A. DE CATALDO
MARK ANDREA A. DE CATALDO*
Affiliation:
Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794-3651, U.S.A e-mail: mark.decataldo@stonybrook.edu
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Abstract

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].

MSC classification

Primary: 14A10: Varieties and morphisms 14D06: Fibrations, degenerations 14D20: Algebraic moduli problems, moduli of vector bundles 14H60: Vector bundles on curves and their moduli
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 172 , Issue 2 , March 2022 , pp. 443 - 487
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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