论文标题
$ \ bar {m} _ {0,7} $的极端除数和特征上的差异2
Extreme Divisors on $\bar{M}_{0,7}$ and Differences over Characteristic 2
论文作者
论文摘要
我们在$ \ bar {m} _ {0,7} $上找到101,052个新的极端分隔线（在31 $ s_7 $ -orbits中）和数百万的极端nef曲线比特征性0。在特征2中，我们确定了两个$ s_7 $ s_7 $ - extretial divisors of Extreme Divisors，provive $ $ $ \ bar c} （\ bar {m} _ {0，n}）$严格比特征2大于特征0，对于所有$ 1 \ leq k \ leq n-6 $。 For each such $k$ we provide explicit cycles which are extreme in $\text{Eff}^k(\bar{M}_{0,n})$ over characteristic 2 but external to $\bar{\text{Eff}}^k(\bar{M}_{0,n})$ over characteristic 0. We apply our method of finding new extreme divisors to compute $ \ text {eff}（\ bar {m} _ {0，\ mathcal {a}}）$ for $ \ mathcal {a} =（\ frac {1} {1} {3} {3}，\ frac {1} {1} {3} {3} {3}，\ frac {1} \ frac {1} {3}，\ frac {1} {3}，1）$，证明它在任何字段上都是多面体，并猜测了$ \ text {eff}的描述{\ text {\ text {bl} _e \ bar bar \ bar {lm} _7）$。
We find 101,052 new extreme divisors on $\bar{M}_{0,7}$ (in 31 $S_7$-orbits) and millions of extreme nef curves over characteristic 0. Over characteristic 2, we identify two more $S_7$-orbits of extreme divisors, and prove $\bar{\text{Eff}}^k (\bar{M}_{0,n})$ is strictly larger over characteristic 2 than it is over characteristic 0, for all $1\leq k \leq n-6$. For each such $k$ we provide explicit cycles which are extreme in $\text{Eff}^k(\bar{M}_{0,n})$ over characteristic 2 but external to $\bar{\text{Eff}}^k(\bar{M}_{0,n})$ over characteristic 0. We apply our method of finding new extreme divisors to compute $\text{Eff}(\bar{M}_{0,\mathcal{A}})$ for $\mathcal{A}=(\frac{1}{3}, \frac{1}{3}, \frac{1}{3}, \frac{1}{3}, \frac{1}{3}, \frac{1}{3}, 1)$, proving it is polyhedral over any field, and conjecture a description of $\text{Eff}(\text{Bl}_e \bar{LM}_7)$.
