On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties

We prove several results concerning the intersection cohomology and the perverse filtration associated with a Lagrangian fibration of an irreducible symplectic variety. We first show that the perverse numbers only depend on the deformation equivalence class of the ambient variety. Then we compute th...

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Bibliographic Details
Main Authors Felisetti, Camilla, Shen, Junliang, Yin, Qizheng
Format Journal Article
LanguageEnglish
Published 05.08.2021
Subjects
Mathematics - Algebraic Geometry
Mathematics - Differential Geometry
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DOI10.48550/arxiv.2108.02464

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Summary:We prove several results concerning the intersection cohomology and the perverse filtration associated with a Lagrangian fibration of an irreducible symplectic variety. We first show that the perverse numbers only depend on the deformation equivalence class of the ambient variety. Then we compute the border of the perverse diamond, which further yields a complete description of the intersection cohomology of the Lagrangian base and the invariant cohomology classes of the fibers. Lastly, we identify the perverse and Hodge numbers of intersection cohomology when the irreducible symplectic variety admits a symplectic resolution. These results generalize some earlier work by the second and third authors in the nonsingular case.
DOI:10.48550/arxiv.2108.02464