Seminars & Colloquia Calendar

Projective duality identifies the moduli space B_n parametrizing configurations of n general points in projective plane with X(3,n), parametrizing configurations of n general lines in the dual plane. When considering degenerations of such objects, it is interesting to compare different compactifications of the above moduli spaces.
In this work, we consider Gerritzen-Piwek's compactification B_n and Kapranov's Chow quotient compactification X(3,n), and we show they have isomorphic normalizations.
We prove that B_n does not admit a modular interpretation claimed by Gerritzen and Piwek, namely a family of n-pointed central fibers of Mustafin joins associated to one-parameter degenerations of n points in the plane. We construct the correct compactification of B_n which admits such a family, and we describe it for n=5,6. This is joint work in progress with Jenia Tevelev.