Algebraic Geometry
Friday, August 30, 2019, 3:15pm, 119 Physics
Luca Schaffler (U Mass)
Compactifications of moduli of points and lines in P²

Abstract:

Projective duality identifies the moduli space B_n parametrizing configurations of n general points in projective 2-space P² with X(3,n), parametrizing configurations of n general lines in the dual P². 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 they have isomorphic normalizations. We also construct an alternative compactification which parametrizes all possible n-pointed central fibers of Mustafin joins associated to one-parameter degenerations of n points in P². This corrects some of the results in Gerritzen-Piwek's paper. Finally, we describe this alternative compactification for n=5,6. This is joint work in progress with Jenia Tevelev.

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