Bogomolov-Sommese vanishing and liftability for surface pairs in positive characteristic
Bogomolov-Sommese vanishing and liftability for surface pairs in positive characteristic
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DOI：
10.1016/j.aim.2022.108640
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发表时间：
2021-08
影响因子：
1.7
通讯作者：
Tatsuro Kawakami
中科院分区：
文献类型：
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作者：
Tatsuro Kawakami
我们证明了除非K X+⌊B⌋的Iitaka维数不等于2，否则对于大特征的对数正则投影曲面（X， B）， Bogomolov-Sommese消失定理是成立的。作为一个应用，我们证明了当对数正则约数的Iitaka维数小于等于零时，法射影曲面和大特征约数对的对数分辨率提升到Witt向量环。此外，除非它们的Iitaka维等于零，否则我们给出了特征的显式和最优边界。
We show that the Bogomolov-Sommese vanishing theorem holds for a log canonical projective surface (X, B) in large characteristic unless the Iitaka dimension of K X+⌊ B⌋ is not equal to two. As an application, we prove that a log resolution of a pair of a normal projective surface and a reduced divisor in large characteristic lifts to the ring of Witt vectors when the Iitaka dimension of the log canonical divisor is less than or equal to zero. Moreover, we give explicit and optimal bounds on the characteristic unless their Iitaka dimensions are equal to zero.