Compactifications of moduli of points and lines in the (tropical) plane

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.

algebraic geometrycombinatorics

Audience: researchers in the topic

Tropical Geometry in Frankfurt/Zoom TGiF/Z

Series comments: Description: An afternoon seminar series on tropical geometry, known as the TGiZ ("Tropical Geometry in Zoom") or the TGiF ("Tropical Geometry in Frankfurt") seminar.

Please send an email to one of the organizers at the latest one day before a session if you wish to receive the Zoom link and password.

Videos of some past talks are available on YouTube here, while some slides can be found here.