Junliang Shen ; Qizheng Yin - Perverse-Hodge complexes for Lagrangian fibrations

epiga:9617 - Épijournal de Géométrie Algébrique, August 21, 2023, Special volume in honour of Claire Voisin - https://doi.org/10.46298/epiga.2023.9617
Perverse-Hodge complexes for Lagrangian fibrationsArticle

Authors: Junliang Shen ; Qizheng Yin

    Perverse-Hodge complexes are objects in the derived category of coherent sheaves obtained from Hodge modules associated with Saito's decomposition theorem. We study perverse-Hodge complexes for Lagrangian fibrations and propose a symmetry between them. This conjectural symmetry categorifies the "Perverse = Hodge" identity of the authors and specializes to Matsushita's theorem on the higher direct images of the structure sheaf. We verify our conjecture in several cases by making connections with variations of Hodge structures, Hilbert schemes, and Looijenga-Lunts-Verbitsky Lie algebras.


    Volume: Special volume in honour of Claire Voisin
    Published on: August 21, 2023
    Accepted on: June 18, 2023
    Submitted on: May 27, 2022
    Keywords: Mathematics - Algebraic Geometry

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