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Creators/Authors contains: "de Cataldo, Mark Andrea"

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  1. ; ; (, Selecta Mathematica)
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  2. ; (, Advances in Mathematics)
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  3. (, Mathematical Proceedings of the Cambridge Philosophical Society)
    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]. 
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  4. ; ; (, Journal de Mathématiques Pures et Appliquées)
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  5. ; ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for GL n {\mathrm{GL}_{n}}over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of reducible spectral curves. Their contribution to the global cohomology is governed by a finite twist of Hitchin fibrations for Levi subgroups. The corresponding summands give non-trivial contributions to the cohomology of the moduli spaces for every n ≥ 2 {n\geq{2}}. A key ingredient is a restriction result for intersection cohomology sheaves that allows us to compare the fibration to the one defined over versal deformations of spectral curves. 
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  6. (, International Mathematics Research Notices)
    Abstract We construct a relative projective compactification of Dolbeault moduli spaces of Higgs bundles for reductive algebraic groups on families of projective manifolds that is compatible with the Hitchin morphism. 
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  7. ; (, Pure and Applied Mathematics Quarterly)
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