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Title:
On isotropic divisors of the Hilbert scheme of K3 surfaces
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Let X be the Hilbert scheme of a K3 surface parametrizing length n scheme and L an isotropic divisor on X. If n is greater than 5, n-1 is odd and n-1 has no square factors, then there exists a projective irreducible symplectic manifold X' which is birational to X and the proper transform L ' of L is free. Moreover L' defines a Lagrangian fibration over the projective space which is deformation equivalent to the compactifield
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