On the Numerical Dimension of Pseudo-Effective Divisors in Positive Characteristic
On the Numerical Dimension of Pseudo-Effective Divisors in Positive Characteristic
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DOI：
10.1353/ajm.2014.0047
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发表时间：
2012-06
影响因子：
1.7
通讯作者：
P. Cascini;Christopher D. Hacon;M. Mustaţă;Karl Schwede
中科院分区：
文献类型：
--
作者：
P. Cascini;Christopher D. Hacon;M. Mustaţă;Karl Schwede
设X是正特征代数闭域上的光滑射影簇。证明了若D是X上的一个伪有效R-因子，且与其因子Zebraki分解中的负部分在数值上不等价，则D的数值维数为正.在特征零中，这是由中山使用消失定理证明的。
Let X be a smooth projective variety over an algebraically closed field of positive characteristic. We prove that if D is a pseudo-effective R-divisor on X which is not numerically equivalent to the negative part in its divisorial Zariski decomposition, then the numerical dimension of D is positive. In characteristic zero, this was proved by Nakayama using vanishing theorems.