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arXiv · 1912.06766

Multiplicativity of perverse filtration for Hilbert schemes of fibered surfaces, II

Zili Zhang
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Abstract

Let $S\to C$ be a smooth quasi-projective surface properly fibered onto a smooth curve. We prove that the multiplicativity of the perverse filtration on $H^*(S^{[n]},\mathbb{Q})$ associated with the natural map $S^{[n]}\to C^{(n)}$ implies that $S\to C$ is an elliptic fibration. The converse is also true when $S\to C$ is a Hitchin-type elliptic fibration.

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Zili Zhang. 2019-12-14. Multiplicativity of perverse filtration for Hilbert schemes of fibered surfaces, II. https://arxiv.org/abs/1912.06766

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