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Jenia Tevelev (University of Massachusetts Amherst)
2021-05-28 14:30 - 15:30 UTC | https://researchseminars.org/talk/TGiZ/26/
Title: Compactifications of moduli of points and lines in the (tropical) plane (https://researchseminars.org/talk/TGiZ/26/)
by Jenia Tevelev (University of Massachusetts Amherst) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z

Abstract
Projective duality identifies moduli spaces of points and lines in the projective plane. The latter space admits Kapranov's Chow quotient compactification, studied also by Lafforgue, Hacking-Keel-Tevelev, and Alexeev, which gives an example of a KSBA moduli space of stable surfaces: it carries a family of reducible degenerations of the projective plane with "broken lines". From the tropical perspective, these degenerations are encoded in matroid decompositions and tropical planes and their moduli space in the Dressian and the tropical Grasmannian. In 1991, Gerritzen and Piwek proposed a dual perspective, a compact moduli space parametrizing reducible degenerations of the projective plane with n smooth points. In a joint paper with Luca Schaffler, we investigate the extension of projective duality to degenerations, answering a question of Kapranov.
