Geodesic
Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces
Journal of Singularities, Tome 7 (2013), pp. 23-38

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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. 
@article{10_5427_jsing_2013_7c,
     author = {Mark Andrea A. de Cataldo and Tam\'as Hausel, and Luca Migliorini},
     title = {Exchange between perverse and weight filtration for the {Hilbert} schemes of points of two surfaces},
     journal = {Journal of Singularities},
     pages = {23--38},
     publisher = {mathdoc},
     volume = {7},
     year = {2013},
     doi = {10.5427/jsing.2013.7c},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2013.7c/}
}
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Mark Andrea A. de Cataldo; Tamás Hausel,; Luca Migliorini. Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. Journal of Singularities, Tome 7 (2013), pp. 23-38. doi: 10.5427/jsing.2013.7c

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