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.

On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties / Felisetti, C.; Shen, J.; Yin, Q.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 375:4(2022), pp. 2987-3001. [10.1090/tran/8592]

On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties

Felisetti C.;
2022

Abstract

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.
2022
375
4
2987
3001
On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties / Felisetti, C.; Shen, J.; Yin, Q.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 375:4(2022), pp. 2987-3001. [10.1090/tran/8592]
Felisetti, C.; Shen, J.; Yin, Q.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1286085
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