English

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

Algebraic Geometry 2014-02-26 v2

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.

Cite

@article{arxiv.0912.3104,
  title  = {Fulton's Conjecture for \bar{M}_{0,7}},
  author = {Paul Larsen},
  journal= {arXiv preprint arXiv:0912.3104},
  year   = {2014}
}

Comments

Proof for n=6 omitted (see instead v1, or Ch. 2 of my thesis: http://edoc.hu-berlin.de/dissertationen/larsen-paul-2010-11-09/PDF/larsen.pdf). Introduction rewritten. Typos corrected. 20 pages. Slightly modified version to appear in the Journal of the London Mathematical Society

R2 v1 2026-06-21T14:24:31.496Z