Topological properties of Hilbert schemes of almost-complex four-manifolds II

Grivaux, Julien¹

¹ Centre de Mathématiques et Informatique, UMR CNRS 6632 (LATP), Université de Provence, 39 rue Frédéric Joliot-Curie, 13453 Cedex 13 Marseille, France

Geometry & topology, Tome 15 (2011) no. 1, pp. 261-330.

Résumé

In this article, we study the rational cohomology rings of Voisin’s Hilbert schemes $X^{\left[n\right]}$ associated with a symplectic compact four-manifold $X$. We prove that these rings can be universally constructed from $H^{\ast }\left(X,\mathbb{Q}\right)$ and $c_1\left(X\right)$, and that Ruan’s crepant resolution conjecture holds if $c_1\left(X\right)$ is a torsion class. Next, we prove that for any almost-complex compact four-manifold $X$, the complex cobordism class of $X^{\left[n\right]}$ depends only on the complex cobordism class of $X$.

Détail

DOI : 10.2140/gt.2011.15.261

Keywords: Hilbert schemes of points, symplectic four-manifold, almost-complex four-manifold, cohomological crepant resolution conjecture

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