Geodesic
Perverse-Hodge complexes for Lagrangian fibrations
Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023)

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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 quot;Perverse = Hodge quot; 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.
DOI : 10.46298/epiga.2023.9617
Classification : 14D06, 14F10, 14J42 
@article{10_46298_epiga_2023_9617,
     author = {Shen, Junliang and Yin, Qizheng},
     title = {Perverse-Hodge complexes for {Lagrangian} fibrations},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     year = {2023},
     doi = {10.46298/epiga.2023.9617},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.9617/}
}
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Shen, Junliang; Yin, Qizheng. Perverse-Hodge complexes for Lagrangian fibrations. Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023). doi: 10.46298/epiga.2023.9617

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