Exceptional Loci on $\bar M_{0,n}$ and Hypergraph Curves

TL;DR

This paper explores special divisors, curves, and morphisms on the moduli space of stable rational curves, using hypergraph-based isomorphisms to reveal unexpected geometric properties.

Contribution

It introduces new extremal divisors and rigid curves on ,n, leveraging hypergraph curves to uncover novel birational phenomena.

Findings

Numerous examples of extremal divisors and rigid curves

Identification of unexpected properties in birational morphisms

Application of hypergraph curves to moduli space geometry

Abstract

We give a myriad of examples of extremal divisors, rigid curves, and birational morphisms with unexpected properties for the Grothendieck--Knudsen moduli space $\bar M_{0,n}$ of stable rational curves. The basic tool is an isomorphism between $M_{0,n}$ and the Brill--Noether locus of a very special reducible curve corresponding to a hypergraph.