The elliptic modular surface of level 4 and its reduction modulo 3
The elliptic modular surface of level 4 and its reduction modulo 3
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4 级椭圆模面及其模 3 的约简
DOI：
10.1007/s10231-019-00927-9
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发表时间：
2020
影响因子：
1
通讯作者：
Ichiro Shimada
中科院分区：
文献类型：
--
作者：
柴崎 貴通;中田 光紀;永田 智久;Ichiro Shimada
第四层的椭圆模曲面是Picard数为20的复K3曲面。这个曲面有一个数域上的模型，使得它的模3约简产生一个与特征为3的费马四次曲面同构的曲面，这是超奇异的。特殊化导致了Néron-Severi格的嵌入。利用这种嵌入，我们确定了特征为3的剩余域的混合特征的离散赋值环上的K3曲面的自同构群。第四层的椭圆模曲面有一个不动点自由对合，它在Nikulin-Kondo-Martin的有限自同构群的Enriques曲面分类中产生了IV型Enriques曲面。我们研究这个对合的特化特征3。
The elliptic modular surface of level 4 is a complexK3 surface with Picard number 20. This surface has a model over a number field such that its reduction modulo 3 yields a surface isomorphic to the Fermat quartic surface in characteristic 3, which is supersingular. The specialization induces an embedding of the Néron–Severi lattices. Using this embedding, we determine the automorphism group of thisK3 surface over a discrete valuation ring of mixed characteristic whose residue field is of characteristic 3. The elliptic modular surface of level 4 has a fixed-point-free involution that gives rise to the Enriques surface of type IV in Nikulin–Kondo–Martin’s classification of Enriques surfaces with finite automorphism group. We investigate the specialization of this involution to characteristic 3.