## Natural $G$-constellation families

### Summary

Summary: 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.

### Mathematics Subject Classification

14J17, 14J10, 14D20, 14J40