Papers › Extreme Divisors on M̅_(0,7) and Differences over Characteristic 2
Extreme Divisors on M̅_(0,7) and Differences over Characteristic 2
Mathieu Dutour Sikirić, Eric Jovinelly
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We find 101,052 new extreme divisors on M̅_(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 E̅f̅f̅ᵏ (M̅_(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 which are extreme in Effᵏ(M̅_(0,n)) over characteristic 2 but external to E̅f̅f̅ᵏ(M̅_(0,n)) over characteristic 0. We apply our method of finding new extreme divisors to compute Eff(M̅_(0,𝒜)) for 𝒜=(1/3, 1/3, 1/3, 1/3, 1/3, 1/3, 1), proving it is polyhedral over any field, and conjecture a description of Eff(Blₑ L̅M̅₇).
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