## Kyoto Journal of Mathematics

### On $G/N$-Hilb of $N$-Hilb

#### Abstract

In this paper we consider the iterated $G$-equivariant Hilbert scheme $G/N$-Hilb($N$-Hilb) and prove that $G/N\mbox{-}\mathrm{Hilb}(N\mbox{-}\mathrm{Hilb}(\mathbb{C}^{3}))$ is a crepant resolution of $\mathbb{C}^{3}/G$ isomorphic to the moduli space $\mathcal{M}_{\theta}(Q)$ of $\theta$-stable representations of the McKay quiver $Q$ for certain stability condition $\theta$. We provide several explicit examples to illustrate this construction. We also consider the problem of when $G/N$-Hilb($N$-Hilb) is isomorphic to $G$-Hilb showing the fact that these spaces are most of the times different.

#### Article information

Source
Kyoto J. Math., Volume 53, Number 1 (2013), 91-130.

Dates
First available in Project Euclid: 25 March 2013

https://projecteuclid.org/euclid.kjm/1364218042

Digital Object Identifier
doi:10.1215/21562261-1966080

Mathematical Reviews number (MathSciNet)
MR3049308

Zentralblatt MATH identifier
1267.14022

#### Citation

Ishii, Akira; Ito, Yukari; Nolla de Celis, Álvaro. On $G/N$ -Hilb of $N$ -Hilb. Kyoto J. Math. 53 (2013), no. 1, 91--130. doi:10.1215/21562261-1966080. https://projecteuclid.org/euclid.kjm/1364218042

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