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Algebra Seminar

Compactifications of moduli of points and lines in the projective plane

Luca Schaffler (U. Mass)

Location:  online
Date & time: Wednesday, 29 April 2020 at 2:00PM - 3:00PM

Projective duality identifies the moduli space Bn 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 Bn and Kapranov's Chow quotient compactification X(3,n), and we show they have isomorphic normalizations.
We prove that Bn 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 Bn which admits such a family, and we describe it for n=5,6. This is joint work in progress with Jenia Tevelev.


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