The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Journal of the European Mathematical Society


Full-Text PDF (213 KB) | Metadata | Table of Contents | JEMS summary
Volume 20, Issue 7, 2018, pp. 1629–1654
DOI: 10.4171/JEMS/795

Published online: 2018-05-22

Homology of Hilbert schemes of points on a locally planar curve

Jørgen Vold Rennemo[1]

(1) All Souls College, Oxford, UK

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.

Keywords: Locally planar curves, Hilbert scheme, compactified Jacobian, Gopakumar– Vafa invariants, Weyl algebra

Vold Rennemo Jørgen: Homology of Hilbert schemes of points on a locally planar curve. J. Eur. Math. Soc. 20 (2018), 1629-1654. doi: 10.4171/JEMS/795