Multiplicativity of Perverse Filtration for Hilbert Schemes of Fibered Surfaces

Zili Zhang

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arXiv · 1512.04643

Multiplicativity of Perverse Filtration for Hilbert Schemes of Fibered Surfaces

Zili Zhang

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Abstract

Let $S\to C$ be a smooth projective surface with numerically trivial canonical bundle fibered onto a curve. We prove the multiplicativity of the perverse filtration with respect to the cup product on $H^*(S^{[n]},\mathbb{Q})$ for the natural morphism $S^{[n]}\to C^{(n)}$. We also prove the multiplicativity for five families of Hitchin systems obtained in a similar way and compute the perverse numbers of the Hitchin moduli spaces. We show that for small values of $n$ the perverse numbers match the predictions of the numerical version of the de Cataldo-Hausel-Migliorini $P=W$ conjecture and of the conjecture by Hausel, Letellier and Rodriguez-Villegas.

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BibTeX RIS

Zili Zhang. 2015-12-15. Multiplicativity of Perverse Filtration for Hilbert Schemes of Fibered Surfaces. https://arxiv.org/abs/1512.04643

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