Extreme Divisors on M‾0,7 and Differences over Characteristic 2

We find 101,052 new extreme divisors on M‾0,7 (in 31 S7-orbits) and millions of extreme nef curves over characteristic 0. Over characteristic 2, we identify two more S7-orbits of extreme divisors and prove Eff‾k(M‾0,n) is strictly larger over characteristic 2 than it is over characteristic 0 for all 1≤k≤n−6. For each such k, we provide explicit cycles that are extreme in Effk(M‾0,n) over characteristic 2 but external to Eff‾k(M‾0,n) over characteristic 0. We apply our method of finding new extreme divisors to compute Eff(M‾0,A) for A=(13,13,13,13,13,13,1), proving it is polyhedral over any field, and conjecture a description of Eff(BleLM‾7).