Perverse-Hodge complexes for Lagrangian fibrations
Perverse-Hodge complexes for Lagrangian fibrations
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DOI：
10.46298/epiga.2023.9617
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发表时间：
2022-01
期刊：
影响因子：
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通讯作者：
Junliang Shen;Qizheng Yin
中科院分区：
文献类型：
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作者：
Junliang Shen;Qizheng Yin
反常-霍奇复形是从与齐藤分解定理相关联的霍奇模获得的相干层的导出范畴中的对象。我们研究反常霍奇复杂的拉格朗日纤维化，并提出了它们之间的对称性。这种结构对称性将作者的“反常=霍奇”身份归类，并专门用于松下关于结构层的高级直接图像的定理。我们验证了我们的猜想在几种情况下，通过与变化的霍奇结构，希尔伯特计划，和Looijenga-Lunts-Verbitsky李代数的连接。
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.