On the QALE geometry of Nakajima's metric.

Gilles Carron (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We show that on Hilbert scheme of $n$ points on $\C^2$, the hyperkähler metric construsted by H. Nakajima via hyperkähler reduction is the Quasi-Asymptotically Locally Euclidean (QALE in short) metric constructed by D. Joyce.

Mots clés: Hyperkaehler manifold; QALE metric; hyperkaehler reduction

Domaines: Géométrie différentielle [math.DG]

Gilles Carron. On the QALE geometry of Nakajima's metric.. Journal of the Institute of Mathematics of Jussieu, 2011, 10, pp.119-147. ⟨hal-00341096⟩