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Lagrangian fibrations on Hilbert schemes of points on \(K3\) surfaces. (English) Zbl 1123.14008

Let \(S\) be a \(K3\) surface whose Picard group equals the integers. If the Picard group is generated by a smooth curve with self-intersection number \(2(g-1)n^2\), then the author shows that the Hilbert scheme of \(g\) points on \(S\) is a Lagrangian fibration. D. Markushevich [Manuscr. Math. 120, No. 2, 131–150 (2006; Zbl 1102.14031)] has obtained similar results, and M. G. Gulbrandsen [Lagrangian fibrations on generalised Kummer varieties, math.AG/0510145] has used similar techniques for generalized Kummer varieties.

MSC:

14D20 Algebraic moduli problems, moduli of vector bundles
14C05 Parametrization (Chow and Hilbert schemes)
14D06 Fibrations, degenerations in algebraic geometry
14J28 \(K3\) surfaces and Enriques surfaces

Citations:

Zbl 1102.14031
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References:

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