Hypertrees, projections, and moduli of stable rational curves

TL;DR

This paper introduces hypertrees, a new combinatorial structure, to describe the effective divisor cone of the moduli space of stable rational curves, revealing new geometric insights.

Contribution

It proposes a conjectural description of the effective divisor cone using hypertrees, connecting combinatorics with algebraic geometry.

Findings

Hypertrees define exceptional divisors with notable properties

Conjectural framework for the effective divisor cone

Bridges combinatorics and moduli space geometry

Abstract

We give a conjectural description for the cone of effective divisors of the Grothendieck-Knudsen moduli space of stable rational curves with n marked points. Namely, we introduce new combinatorial structures called hypertrees and show they give exceptional divisors with many remarkable properties.