Lagrangian fibrations on Hilbert schemes of points on K3 surfaces

Abstract:

Let Hilb^gS be the Hilbert scheme of g points on a K3 surface S. Suppose that PicS=Z[C] where C is a smooth curve with C^2=2(g-1)n^2. We prove that Hilb^gS is a Lagrangian fibration.

Appears in Volume 17 (2007) No. 3 of the Journal of Algebraic Geometry, pages 477-497. Available as math.AG/0509224 from the e-Print archive.

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