Volume 15, issue 1 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
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