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.

Voir la notice de l'article provenant de la source EMS Press

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
Mots-clés : 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},
     publisher = {mathdoc},
     volume = {20},
     number = {7},
     year = {2018},
     doi = {10.4171/jems/795},
     url = {https://geodesic-test.mathdoc.fr/articles/10.4171/jems/795/}
}
TY  - JOUR
AU  - Jørgen Vold Rennemo
TI  - Homology of Hilbert schemes of points on a locally planar curve
JO  - Journal of the European Mathematical Society
PY  - 2018
SP  - 1629
EP  - 1654
VL  - 20
IS  - 7
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.4171/jems/795/
DO  - 10.4171/jems/795
ID  - JEMS_2018_20_7_a2
ER  - 
%0 Journal Article
%A Jørgen Vold Rennemo
%T Homology of Hilbert schemes of points on a locally planar curve
%J Journal of the European Mathematical Society
%D 2018
%P 1629-1654
%V 20
%N 7
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.4171/jems/795/
%R 10.4171/jems/795
%F JEMS_2018_20_7_a2
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. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/795/

Cité par Sources :