尖点有理曲线自乘积的Kummer曲面
Kummer surfaces for the selfproduct of the cuspidal rational curve
AI总结：
针对特征2下经典Kummer构造对超奇异阿贝尔曲面失效的问题，本文用有理尖点曲线自乘积和无穷小群概型作用给出新的Kummer型构造，得到Artin不变量为1、2的超奇异K3曲面，它们属于纯不可分基变换后同步消解得到的1维族。
摘要：
经典Kummer构造可从一个阿贝尔曲面得到一个K3曲面。正如Shioda与Katsura所证明的，该构造在特征为2的超奇异阿贝尔曲面情形下失效。本文用有理尖点曲线的自乘积替代超奇异阿贝尔曲面，用合适的无穷小群概型作用替代符号对合，给出了该情形下正确的Kummer型构造。我们遇到的是D_4型与D_8型有理二重点，而非A_1型。结果表明，所得曲面是Artin不变量为1和2的超奇异K3曲面，它们属于一个1维族，该族通过纯不可分基变换后的同步消解得到。
英文摘要：
The classical Kummer construction attaches to an abelian surface a K3 surface. As Shioda and Katsura showed, this construction breaks down for supersingular abelian surfaces in characteristic two. Replacing supersingular abelian surfaces by the selfproduct of the rational cuspidal curve, and the sign involution by suitable infinitesimal group scheme actions, I give the correct Kummer-type construction in this situation. We encounter rational double points of type D_4 and D_8, instead of type A_1. It turns out that the resulting surfaces are supersingular K3 surfaces with Artin invariant one and two. They lie in a 1-dimensional family obtained by simultaneous resolution after purely inseparable base change.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
