Natural G-Constellation Families

Details Natural G-Constellation Families Natural G-Constellation Families

2005-12-31

arxiv.org/abs/math/0601014v2

Mathematics

Algebraic Geometry

19 pages; v2.0, minor corrections, re-written introduction; to appear in Documenta Mathematica

Scientific paper

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

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