Geodesic
Homology of Hilbert schemes of points on a locally planar curve
Journal of the European Mathematical Society, Tome 20 (2018) no. 7, pp. 1629-1654 Cet article a éte moissonné depuis la source EMS Press

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Let C be a proper, integral, locally planar curve, and consider its Hilbert schemes of points C[n]. We define four creation/annihilation operators acting on the rational homology groups of these Hilbert schemes and show that the operators satisfy the relations of a Weyl algebra. The action of this algebra is similar to that defined by Grojnowski and Nakajima for a smooth surface. As a corollary, we compute the cohomology of C[n] in terms of the cohomology of the compactified Jacobian of C together with an auxiliary grading on the latter. This recovers and slightly strenghtens a formula recently obtained in a different way by Maulik and Yun and independently Migliorini and Shende.
DOI : 10.4171/jems/795
Classification : 14-XX
Keywords: Locally planar curves, Hilbert scheme, compactified Jacobian, Gopakumar– Vafa invariants, Weyl algebra 
@article{JEMS_2018_20_7_a2,
     author = {J{\o}rgen Vold Rennemo},
     title = {Homology of {Hilbert} schemes of points on a locally planar curve},
     journal = {Journal of the European Mathematical Society},
     pages = {1629--1654},
     year = {2018},
     volume = {20},
     number = {7},
     doi = {10.4171/jems/795},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/795/}
}
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Jørgen Vold Rennemo. Homology of Hilbert schemes of points on a locally planar curve. Journal of the European Mathematical Society, Tome 20 (2018) no. 7, pp. 1629-1654. doi: 10.4171/jems/795

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