A note on the supersingular \(K3\) surface of Artin invariant 1
This paper is concerned with the supersingular \(K3\) surface \(X\) of Artin invariant \(1\) in characteristic \(p>0\), where \(p\) is an arbitrary prime. Over the algebraic closure \(\overline{{\mathbb{F}}_p}\), such a \(K3\) surface is unique. The main result is this paper is the following theorem.NEWLINENEWLINETheorem. The supersingular \(K3\) surface \(X\) with Artin invariant \(1\) admits a model over the prime field \({\mathbb{F}}_p\) with Picard number \(21\).NEWLINENEWLINEThis model attains the Picard number \(22\) over the quadratic extension \({\mathbb{F}}_{p^2}\), but this maximum can never attained over \({\mathbb{F}}_{p^e}\) for any odd \(e\).
scientific article; zbMATH DE number 6094130
scientific article