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Lagrangian fibrations on Hilbert schemes of points on K3 surfaces

Justin Sawon
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Abstract

Let $\mathrm{Hilb}^gS$ be the Hilbert scheme of $g$ points on a K3 surface $S$. Suppose that $\mathrm{Pic}S\cong\Z C$ where $C$ is a smooth curve with $C^2=2(g-1)n^2$. We prove that $\mathrm{Hilb}^gS$ is a Lagrangian fibration.

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Justin Sawon. 2005-10-07. Lagrangian fibrations on Hilbert schemes of points on K3 surfaces. https://arxiv.org/abs/math/0509224

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