Degeneration of point configurations in the projective plane

Abstract

AbstractIn this paper we construct a compactification of the moduli space Bn∗=(P22⧹Δ)⧸PGL(3)of n-point configuration in the plane in general position modulo linear transformations. This compactification Bn is an analogue to the space of n-pointed trees of projective lines and a generalization of a compactification of orbit spaces of more general group actions. We relate the fibres of the universal n-point configuration Fn→Bn to schemes associated with the Bruhat-Tits Building and give explicit descriptions in the cases n=5 and n=6