Natural \(G\)-constellation families (Q2517775)

Summary: Let \(G\) be a finite subgroup of \(\text{GL}_n(\mathbb{C})\). \(G\)-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.