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

Mark Andrea A. de Cataldo, Tamás Hausel, and Luca Migliorini

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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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.

Author(s) information:

Mark Andrea A. de Cataldo Tamás Hausel Luca Migliorini
Department of Mathematics Section de Mathématiques Dipartimento di Matematica
SUNY at Stony Brook École Polytechnique Fédérale de Lausanne Università di Bologna
Stony Brook, NY 11794, USA Station 8 Piazza di Porta S. Donato 5
CH-1015 Lausanne, SWITZERLAND 40126 Bologna, ITALY
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