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arXiv · 1108.2310

On G/N-Hilb of N-Hilb

Akira Ishii·Yukari Ito·Álvaro Nolla de Celis
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Abstract

In this paper we consider the iterated G-equivariant Hilbert scheme G/N-Hilb(N-Hilb) and prove that G/N-Hilb(N-Hilb(C^3)) is a crepant resolution of C^3/G isomorphic to the moduli space of \theta-stable representations of the McKay quiver 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.

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Akira Ishii, Yukari Ito, Álvaro Nolla de Celis. 2011-08-11. On G/N-Hilb of N-Hilb. https://doi.org/10.1215/21562261-1966080

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