Fulton's Conjecture for \bar{M}_{0,7}

TL;DR

This paper proves Fulton's conjecture for the moduli space of stable rational curves with seven marked points, showing that certain divisors are equivalent to effective sums of boundary divisors.

Contribution

The authors establish Fulton's conjecture for n=7 and introduce a new inom{n}{4}-dimensional subspace of the Neron-Severi space where the conjecture holds.

Findings

Proof of Fulton's conjecture for n=7

Identification of a new subspace where the conjecture is valid

Validation of the conjecture for all n within this subspace

Abstract

Fulton's conjecture for the moduli space of stable pointed rational curves, \bar{M}_{0,n}, claims that a divisor non-negatively intersecting all F-curves is linearly equivalent to an effective sum of boundary divisors. Our main result is a proof of Fulton's conjecture for n=7. A key ingredient in the proof is an \binom{n}{4} dimensional-subspace of the Neron-Severi space of \bar{M}_{0,n}, defined by averages of Keel relations, for which we prove Fulton's conjecture for all n.