Lazy tournaments, slide rules, and multidegrees of projective embeddings of M_{0,n}-bar

Abstract: We present a combinatorial algorithm on trivalent trees that we call a lazy tournament, which gives rise to a new geometric interpretation of the multidegrees of a projective embedding of the moduli space M_{0,n}-bar of stable n-marked genus 0 curves. We will show that the multidegrees are enumerated by disjoint sets of boundary points of the moduli space that can be seen to total (2n-7)!!, giving a natural proof of the value of the total degree. These sets are compatible with the forgetting maps used to derive the previously known recursion for the multidegrees.

As time permits, we will discuss an alternative combinatorial construction of (non-disjoint) sets of boundary points that enumerate the multidegrees, via slide rules, that can in fact be achieved geometrically via a degeneration of intersections with hyperplanes in the projective embedding. These combinatorial rules further generalize to give a positive expansion of any product of psi or omega classes on M_{0,n}-bar in terms of boundary strata.

This is joint work with Sean Griffin and Jake Levinson.

algebraic geometrynumber theory

Audience: researchers in the topic

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SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca

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