Pathologies and liftability of Du Val del Pezzo surfaces in positive characteristic
Pathologies and liftability of Du Val del Pezzo surfaces in positive characteristic
复制标题
DOI：
10.1007/s00209-022-02998-6
复制
发表时间：
2020-08
影响因子：
0.8
通讯作者：
Tatsuro Kawakami;Masaru Nagaoka
中科院分区：
文献类型：
--
作者：
Tatsuro Kawakami;Masaru Nagaoka
本文研究了定义在具有正特征的代数闭域上的Du Val del Pezzo曲面的病理学，将它们与其在Witt向量环上的不可升性联系起来。更确切地说，我们研究了条件(NB)：所有反正则因子都是奇异的，(ND)：复数域上不存在具有相同的动态金型、Picard秩和反正则度的Du Val del Pezzo曲面，(NK)：存在一个充分因子，它违反了-因子的Kodaira消失定理，以及(NL)：(Y，E)对(Y，E)不提升到Witt向量环，其中Y是最小分辨率，E是它的约化例外因子。因此，对于每个条件，我们确定了满足给定条件的所有Du Val del Pezzo曲面。
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-divisor which violates the Kodaira vanishing theorem for-divisors, and (NL): the pair (Y,E) does not lift to the ring of Witt vectors, whereYis the minimal resolution andEis 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.