Lagrangian fibrations on Hilbert schemes of points on K3 surfaces

Details Lagrangian fibrations on Hilbert schemes of points on K3 surfaces Lagrangian fibrations on Hilbert schemes of points on K3 surfaces

2005-09-09

arxiv.org/abs/math/0509224v3

J. Algebraic Geom. 16 (2007), no. 3, 477-497

Mathematics

Algebraic Geometry

21 pages, original (stronger) version of Theorem 2 proved

Scientific paper

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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