Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces

Journal of Singularities
volume 7 (2013), 23-38

Received: 25 February 2012. Received in revised form: 26 February 2013.

DOI: 10.5427/jsing.2013.7c

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Abstract:

We show that a natural isomorphism between the rational cohomology groups of the two zero-dimensional Hilbert schemes of n-points of two surfaces, the affine plane minus the axes and the cotangent bundle of an elliptic curve, exchanges the weight filtration on the first set of cohomology groups with the perverse Leray filtration associated with a natural fibration on the second set of cohomology groups. We discuss some associated hard Lefschetz phenomena.

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