Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Lagrangian fibrations on Hilbert schemes of points on K3 surfaces


Author: Justin Sawon
Journal: J. Algebraic Geom. 16 (2007), 477-497
DOI: https://doi.org/10.1090/S1056-3911-06-00453-X
Published electronically: December 6, 2006
MathSciNet review: 2306277
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Abstract | References | Additional Information

Abstract: Let $ \mathrm{Hilb}^gS$ be the Hilbert scheme of $ g$ points on a K3 surface $ S$. Suppose that $ \mathrm{Pic}S\cong\mathbb{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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Additional Information

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

DOI: https://doi.org/10.1090/S1056-3911-06-00453-X
Received by editor(s): September 10, 2005
Received by editor(s) in revised form: February 22, 2006
Published electronically: 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.

American Mathematical Society