Nolan Shock : Geometry of tropical compactifications of moduli spaces

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

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Feb. 28, 2022, 3 p.m.

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Abstract

The Grothendieck-Knudsen compactification of the moduli space of n-pointed rational curves satisfies a number of remarkable properties: it has a modular interpretation (by construction), it is the log canonical compactification (roughly, the smallest compactification with reasonable boundary singularities), and its Chow ring is the same as its cohomology ring and looks like the Chow ring/cohomology ring of a toric variety. I will discuss how these results can be partially generalized to compactifications of moduli of higher-dimensional varieties (namely, moduli of hyperplane arrangements and marked del Pezzo surfaces) by using some simple ideas in tropical geometry.