Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces
De Cataldo M, Hausel T, Migliorini L. 2013. Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. Journal of Singularities. 7, 23–38.
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Author
De Cataldo, Mark A;
Hausel, TamasISTA;
Migliorini, Luca
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.
Publishing Year
Date Published
2013-01-01
Journal Title
Journal of Singularities
Publisher
Worldwide Center of Mathematics
Acknowledgement
Mark Andrea A. de Cataldo was partially supported by N.S.A. and N.S.F. Tamás Hausel was supported by a Royal Society University Research Fellowship. Luca Migliorini was partially supported by PRIN 2007 project "Spazi di moduli e teoria di Lie"
Volume
7
Page
23 - 38
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Cite this
De Cataldo M, Hausel T, Migliorini L. Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. Journal of Singularities. 2013;7:23-38. doi:10.5427/jsing.2013.7c
De Cataldo, M., Hausel, T., & Migliorini, L. (2013). Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. Journal of Singularities. Worldwide Center of Mathematics. https://doi.org/10.5427/jsing.2013.7c
De Cataldo, Mark, Tamás Hausel, and Luca Migliorini. “Exchange between Perverse and Weight Filtration for the Hilbert Schemes of Points of Two Surfaces.” Journal of Singularities. Worldwide Center of Mathematics, 2013. https://doi.org/10.5427/jsing.2013.7c.
M. De Cataldo, T. Hausel, and L. Migliorini, “Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces,” Journal of Singularities, vol. 7. Worldwide Center of Mathematics, pp. 23–38, 2013.
De Cataldo M, Hausel T, Migliorini L. 2013. Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. Journal of Singularities. 7, 23–38.
De Cataldo, Mark, et al. “Exchange between Perverse and Weight Filtration for the Hilbert Schemes of Points of Two Surfaces.” Journal of Singularities, vol. 7, Worldwide Center of Mathematics, 2013, pp. 23–38, doi:10.5427/jsing.2013.7c.
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