论文标题
阳性特征中杜瓦尔·德·佩佐表面的病理和升高性
Pathologies and liftability of Du Val del Pezzo surfaces in positive characteristic
论文作者
论文摘要
在本文中，我们研究了杜瓦尔·德·佩佐表面的病理学，该表面在代数封闭的积极特征上定义了，通过将它们与witt载体的不可贴性联系起来。更准确地说，我们研究了条件（NB）：所有反典型的分隔线都是单数的，（nd）：在复数的领域，没有同一dynkin型，PICARD等级，Picard等级和反典型学位的du val del del pezzo表面，（NK）。 $ \ mathbb {z} $ - 除数和（nl）：这对$（y，e）$不提升到witt矢量的戒指，其中$ y $是最小的分辨率，而$ e $是其降低的出色分数。结果，对于每种条件，我们确定满足给定的所有du val del del pezzo表面。
In this paper, we study pathologies of Du Val del Pezzo surfaces defined over an algebraically closed field of positive characteristic by relating them to their non-liftability to the ring of Witt vectors. More precisely, we investigate the condition (NB): all the anti-canonical divisors are singular, (ND): there are no Du Val del Pezzo surfaces over the field of complex numbers with the same Dynkin type, Picard rank, and anti-canonical degree, (NK): there exists an ample $\mathbb{Z}$-divisor which violates the Kodaira vanishing theorem for $\mathbb{Z}$-divisors, and (NL): the pair $(Y, E)$ does not lift to the ring of Witt vectors, where $Y$ is the minimal resolution and $E$ is its reduced exceptional divisor. As a result, for each of these conditions, we determine all the Du Val del Pezzo surfaces which satisfy the given one.
