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Fulton's conjecture for the moduli space of stable pointed rational curves,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(    n  4    )‐dimensional subspace of the Néron–Severi space ofM  ¯0  ,  n, defined by averages of Keel relations, for which we prove Fulton's conjecture for all  n .

Fulton's conjecture for M̅ 0,7