Natural G-Constellation Families

Let $G$ be a finite subgroup of $\gl_n(\mathbb{C})$. $G$-constellations are a scheme-theoretic generalization of orbits of $G$ in $\mathbb{C}^n$. We study flat families of $G$-constellations parametrised by an arbitrary resolution of the quotient space $\mathbb{C}^n/G$. We develop a geometrical naturality criterion for such families, and show that, for an abelian $G$, the number of equivalence classes of these natural families is finite. The main intended application is the derived McKay correspondence.

2000 Mathematics Subject Classification: Primary 14J17; Secondary 14J10, 14D20, 14J40.

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