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arXiv · 2503.14890

Perverse-Hodge complexes for Lagrangian fibrations and symplectic resolutions

Zhengze Xin
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Abstract

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.

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Zhengze Xin. 2025-03-19. Perverse-Hodge complexes for Lagrangian fibrations and symplectic resolutions. https://arxiv.org/abs/2503.14890

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