Journal of Algebraic Geometry

Author(s): Justin Sawon
Journal: J. Algebraic Geom. 16 (2007), 477-497.
Posted: December 6, 2006
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Abstract: Let $\mathrm{Hilb}^gS$ be the Hilbert scheme of

points on a K3 surface

. Suppose that $\mathrm{Pic}S\cong\mathbb{Z}C$ where

is a smooth curve with

. We prove that $\mathrm{Hilb}^gS$ is a Lagrangian fibration.

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Justin Sawon
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651
Address at time of publication: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523-1874
Email: sawon@math.sunysb.edu; sawon@math.colostate.edu

PII: S 1056-3911(06)00453-X
Received by editor(s): September 10, 2005
Received by editor(s) in revised form: February 22, 2006
Posted: December 6, 2006
Additional Notes: The author is grateful for the hospitality of the Johannes-Gutenberg Universität, Mainz, where this article was written. The author is supported by NSF grant number 0305865.

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