# Luca Schaffler: Compactifications of moduli of points and lines in the projective plane

**Time: **
Wed 2020-11-18 13.15 - 14.15

**Location: **
Zoom, meeting ID: 657 9019 8929

**Participating: **
Luca Schaffler, KTH

### Abstract

Projective duality identifies the moduli space \(B_n\) parametrizing configurations of \(n\) general points in the projective plane with \(X(3,n)\), parametrizing configurations of \(n\) general lines in the dual projective 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 of \(B_n\) and Kapranov's Chow quotient compactification of \(X(3,n)\), and we show that they have isomorphic normalizations. We also construct an alternative compactification parametrizing all possible \(n\)-pointed central fibers of Mustafin joins associated to one-parameter degenerations of \(n\) points in the projective plane, which was proposed by Gerritzen and Piwek. We fully describe this alternative compactification for \(n=5,6\). This is joint work with Jenia Tevelev.

**Zoom Notes: **The meeting ID is 657 9019 8929 and the passcode is 3517257.