Volume 15, issue 1 (2011)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Topological properties of Hilbert schemes of almost-complex four-manifolds II

Julien Grivaux

Geometry & Topology 15 (2011) 261–330
Abstract

In this article, we study the rational cohomology rings of Voisin’s Hilbert schemes X[n] associated with a symplectic compact four-manifold X. We prove that these rings can be universally constructed from H(X, ) and c1(X), and that Ruan’s crepant resolution conjecture holds if c1(X) is a torsion class. Next, we prove that for any almost-complex compact four-manifold X, the complex cobordism class of X[n] depends only on the complex cobordism class of X.

Keywords
Hilbert schemes of points, symplectic four-manifold, almost-complex four-manifold, cohomological crepant resolution conjecture
Mathematical Subject Classification 2000
Primary: 32Q60
Secondary: 14C05, 14J35
References
Publication
Received: 29 June 2009
Revised: 13 September 2010
Accepted: 13 November 2010
Published: 14 February 2011
Proposed: Lothar Göttsche
Seconded: Richard Thomas, Jim Bryan
Authors
Julien Grivaux
Centre de Mathématiques et Informatique
UMR CNRS 6632 (LATP)
Université de Provence
39 rue Frédéric Joliot-Curie
13453 Cedex 13 Marseille
France