On G/N-Hilb of N-Hilb

Details On G/N-Hilb of N-Hilb On G/N-Hilb of N-Hilb

2011-08-11

arxiv.org/abs/1108.2310v1

Mathematics

Algebraic Geometry

Scientific paper

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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