Kyoto Journal of Mathematics

On G/N-Hilb of N-Hilb

Akira Ishii, Yukari Ito, and Álvaro Nolla de Celis

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In this paper we consider the iterated G-equivariant Hilbert scheme G/N-Hilb(N-Hilb) and prove that G/N-Hilb(N-Hilb(C3)) is a crepant resolution of C3/G isomorphic to the moduli space Mθ(Q) of θ-stable representations of the McKay quiver Q for certain stability condition θ. 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.

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

First available in Project Euclid: 25 March 2013

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Zentralblatt MATH identifier

Primary: 14E16: McKay correspondence
Secondary: 14C05: Parametrization (Chow and Hilbert schemes) 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14E15: Global theory and resolution of singularities [See also 14B05, 32S20, 32S45] 16G20: Representations of quivers and partially ordered sets


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.

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