An Enriques Involution of a Supersingular K3 Surface Over Odd Characteristic

作者：Jang Junmyeong^*

来源：International Mathematics Research Notices, 2014, 2014(11): 3158-3175.

DOI：10.1093/imrn/rnt248

A complex K3 surface has an Enriques involution if and only if there exists a primitive embedding of the scalar multiple by 2 of the Enriques lattice into the Neron-Severi lattice such that the orthogonal complement of the embedding has no vector of self-intersection -2 [11]. In the proof of this criterion the Torelli theorem for K3 surfaces is used. In this paper, we prove that the same criterion holds for supersingular K3 surfaces defined over a field of odd characteristic using the crystalline Torelli theorem. From this criterion, we also prove that, over a field of characteristic p = 19 or p %26gt; 23, a supersingular K3 surface is an Enriques K3 surface if and only if the Artin invariant is %26lt;6.

• 出版日期2014