Algebra-Geometry-Combinatorics Seminar

Speaker: Deniz Genlik, UIUC

Title: Polytopes of Effective Boundary Expressions of Divisors on $\bar{M}_{0,n}$

Abstract: The moduli space $\bar{M}_{0,n}$ parametrizes stable rational curves with 𝑛 marked points. Its boundary divisors generate the divisor class group, so every divisor class can be written (generally non-uniquely) as a linear combination of boundary divisor classes. For a fixed divisor class [𝐷], the collection of its effective boundary expressions forms a polytope. In this talk, I will describe these polytopes and for several natural divisor classes I will explain their connections with classical objects in graph theory and combinatorial optimization, including spanning trees and forests, Hamiltonian cycles, perfect matchings, and Turán graphs. These connections also produce new combinatorial formulas for these natural divisor classes on $\bar{M}_{0,n}$. This is joint work with Ian Cavey.