Homology of Hilbert schemes of points on a locally planar curve

Jørgen Vold Rennemo

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arXiv · 1308.4104

Homology of Hilbert schemes of points on a locally planar curve

Jørgen Vold Rennemo

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Abstract

Let C be a proper, integral, locally planar curve, and consider its Hilbert schemes of points C^[n]. We define 4 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.

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BibTeX RIS

Jørgen Vold Rennemo. 2013-08-19. Homology of Hilbert schemes of points on a locally planar curve. https://arxiv.org/abs/1308.4104

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