Lazy tournaments for the multidegrees of $$\overline{M_{0,n}}$$

event Friday, May 7, 2021
access_time 3:30pm (CDT)
room Zoom
free_breakfast Tea at 4:30pm (CDT) on Zoom

Abstract: The moduli space $$\overline{M_{0,n}}$$ parametrizes of genus 0 stable curves with n marked points. Geometrically, such a curve is a tree structure of $$\mathbb{P}^1$$'s joined at simple nodes. Kapranov gave a natural projective embedding $$\overline{M_{0,n}} \to \mathbb{P}^{n-3} \times \overline{M_{0,n-1}}$$, essentially an embedding of the universal curve. And, iterating this construction embeds the moduli space in a product of projective spaces, $$\mathbb{P}^{n-3} \times \mathbb{P}^{n-4} \times \cdots \times \mathbb{P}^1$$. The multidegrees of this embedding (coefficients for the cohomology class of the image) have interesting combinatorial meaning. I'll discuss some combinatorial rules for describing them in terms of "lazy tournaments" on trees. One consequence is an elegant explanation for why the sum of the multidegrees is the odd double factorial. This is joint work with Maria Gillespie and Sean Griffin.