Perverse-Hodge complexes for Lagrangian fibrations and symplectic resolutions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908274739118080 |
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| author | Xin, Zhengze |
| author_facet | Xin, Zhengze |
| contents | We study perverse-Hodge complexes for Lagrangian fibrations on holomorphic symplectic varieties. We prove the symplectic Hard Lefschetz type theorem and the symmetry of perverse-Hodge complexes when the symplectic variety admits symplectic resolutions, therefore generalize the previous result by Schnell in the smooth case verifying a conjecture by Shen-Yin. Along the way, we study the perverse coherent properties of the intersection complex Hodge modules on symplectic varieties. As an application, we obtain an alternative proof of the numerical "perverse=Hodge" result by Felisetti-Shen-Yin, without using the Beauville-Bogomolov-Fujiki form. We also apply our results to study singular Higgs moduli spaces over reduced curves using results by Mauri-Migliorini on the local structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Perverse-Hodge complexes for Lagrangian fibrations and symplectic resolutions Xin, Zhengze Algebraic Geometry We study perverse-Hodge complexes for Lagrangian fibrations on holomorphic symplectic varieties. We prove the symplectic Hard Lefschetz type theorem and the symmetry of perverse-Hodge complexes when the symplectic variety admits symplectic resolutions, therefore generalize the previous result by Schnell in the smooth case verifying a conjecture by Shen-Yin. Along the way, we study the perverse coherent properties of the intersection complex Hodge modules on symplectic varieties. As an application, we obtain an alternative proof of the numerical "perverse=Hodge" result by Felisetti-Shen-Yin, without using the Beauville-Bogomolov-Fujiki form. We also apply our results to study singular Higgs moduli spaces over reduced curves using results by Mauri-Migliorini on the local structure. |
| title | Perverse-Hodge complexes for Lagrangian fibrations and symplectic resolutions |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2503.14890 |