On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties
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- by Camilla Felisetti, Junliang Shen and Qizheng Yin PDF
- Trans. Amer. Math. Soc. 375 (2022), 2987-3001 Request permission
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.References
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Additional Information
- Camilla Felisetti
- Affiliation: Department of Mathematics, University of Trento, Trento TN, Italy
- MR Author ID: 1423246
- ORCID: 0000-0001-9255-7866
- Email: camilla.felisetti@unitn.it
- Junliang Shen
- Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut
- MR Author ID: 1134436
- Email: junliang.shen@yale.edu
- Qizheng Yin
- Affiliation: Peking University, Beijing, China
- MR Author ID: 1110022
- Email: qizheng@math.pku.edu.cn
- Received by editor(s): September 1, 2021
- Received by editor(s) in revised form: November 3, 2021, and November 5, 2021
- Published electronically: January 20, 2022
- Additional Notes: The first author was supported by PRIN 2017 “Moduli Theory and Birational Classification” and GNSAGA. The second author was supported by the NSF grant DMS 2134315. The third author was supported by the NSFC grants 11831013 and 11890661
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 2987-3001
- MSC (2020): Primary 14J42, 14D06; Secondary 32S35
- DOI: https://doi.org/10.1090/tran/8592
- MathSciNet review: 4391739