{"doi":"10.5427/jsing.2013.7c","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\"","abstract":[{"lang":"eng","text":"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."}],"publisher":"Worldwide Center of Mathematics","status":"public","month":"01","publist_id":"5725","_id":"1470","type":"journal_article","author":[{"first_name":"Mark","last_name":"De Cataldo","full_name":"De Cataldo, Mark A"},{"full_name":"Tamas Hausel","last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamas"},{"full_name":"Migliorini, Luca","first_name":"Luca","last_name":"Migliorini"}],"page":"23 - 38","title":"Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces","intvolume":"         7","date_updated":"2021-01-12T06:50:58Z","quality_controlled":0,"publication_status":"published","volume":7,"publication":"Journal of Singularities","date_created":"2018-12-11T11:52:12Z","day":"01","date_published":"2013-01-01T00:00:00Z","citation":{"mla":"De Cataldo, Mark, et al. “Exchange between Perverse and Weight Filtration for the Hilbert Schemes of Points of Two Surfaces.” <i>Journal of Singularities</i>, vol. 7, Worldwide Center of Mathematics, 2013, pp. 23–38, doi:<a href=\"https://doi.org/10.5427/jsing.2013.7c\">10.5427/jsing.2013.7c</a>.","short":"M. De Cataldo, T. Hausel, L. Migliorini, Journal of Singularities 7 (2013) 23–38.","chicago":"De Cataldo, Mark, Tamás Hausel, and Luca Migliorini. “Exchange between Perverse and Weight Filtration for the Hilbert Schemes of Points of Two Surfaces.” <i>Journal of Singularities</i>. Worldwide Center of Mathematics, 2013. <a href=\"https://doi.org/10.5427/jsing.2013.7c\">https://doi.org/10.5427/jsing.2013.7c</a>.","ista":"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.","ama":"De Cataldo M, Hausel T, Migliorini L. Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. <i>Journal of Singularities</i>. 2013;7:23-38. doi:<a href=\"https://doi.org/10.5427/jsing.2013.7c\">10.5427/jsing.2013.7c</a>","ieee":"M. De Cataldo, T. Hausel, and L. Migliorini, “Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces,” <i>Journal of Singularities</i>, vol. 7. Worldwide Center of Mathematics, pp. 23–38, 2013.","apa":"De Cataldo, M., Hausel, T., &#38; Migliorini, L. (2013). Exchange between perverse and weight filtration for the Hilbert schemes of points of two surfaces. <i>Journal of Singularities</i>. Worldwide Center of Mathematics. <a href=\"https://doi.org/10.5427/jsing.2013.7c\">https://doi.org/10.5427/jsing.2013.7c</a>"},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1012.2583"}],"extern":1,"oa":1,"year":"2013"}