椭圆纤维化K3曲面的镜像
代数几何
2017-02-28 v2
摘要
我们研究一个双参数族的（一般）Picard秩为的K3曲面，它镜像于带截面的椭圆纤维化K3曲面的维族。该族的成员由三维代数环面中由方程给出的超曲面的紧化给出，其中和为该族的参数。由Morrison先前的工作可知，这些曲面是来自椭圆曲线乘积的Kummer曲面的二重覆盖，我们显式地建立了这一联系。这进而给出了镜像于Picard秩为1的极化K3曲面的单参数K3曲面族的描述。我们已获悉本文结果已见于现有文献，相应的参考文献已添加在引言末尾。
引用
@article{arxiv.1702.03919,
title = {On mirrors of elliptically fibered K3 surfaces},
author = {Lev Borisov},
journal= {arXiv preprint arXiv:1702.03919},
year = {2017}
}
备注
It was brought to our attention that the results are well known to the experts. Specifically, the results appear in the work of T. Shioda as well as A. Clingher and C. Doran. The appropriate comments are made in the new abstract and at the end of the introduction