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

Abstract : In this article, we study the rational cohomology rings of Voisin's punctual Hilbert schemes $X^{[n]}$ associated to a symplectic compact fourfold $X$. We prove that these rings can be universally constructed from $H^*(X,\mathbb{Q})$ and $c_1(X)$, and that Ruan's crepant resolution conjecture holds if $c_1(X)$ is a torsion class. Next, we prove that for any almost-complex compact fourfold $X$, the complex cobordism class of $X^{[n]}$ depends only on the cobordism class of $X$.
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Julien Grivaux. Topological properties of Hilbert schemes of almost-complex four-manifolds II. Geometry and Topology, Mathematical Sciences Publishers, 2011, 15 (1), pp.261-330. ⟨10.2140/gt.2011.15.261⟩. ⟨hal-01301345⟩

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