Topological properties of Hilbert schemes of almost-complex fourfolds (I)

Julien Grivaux (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

In this article, we study topological properties of Voisin's punctual Hilbert schemes of an almost-complex fourfold X. In this setting, we compute their Betti numbers and construct Nakajima operators. We also define tautological bundles associated with any complex bundle on X, which are shown to be canonical in K-theory.

Mots clés: almost-complex four-manifold; symplectic four-manifold; Hilbert schemes of points; cohomological crepant resolution conjecture

Domaines: Géométrie algébrique [math.AG]; Géométrie symplectique [math.SG]

Julien Grivaux. Topological properties of Hilbert schemes of almost-complex fourfolds (I). Manuscripta mathematica, 2011, 136 (1-2), pp.155-184. ⟨10.1007/s00229-011-0435-z⟩. ⟨hal-01301361⟩