论文标题
关于超代理K3表面的Enriques的数量
On the number of Enriques quotients for supersingular K3 surfaces
论文作者
论文摘要
我们表明，大多数K3表面的类别只有许多Enriques的商品有限。对于特征性$ p \ geq 3 $领域上的超高k3表面，我们给出了一个公式，该公式通常会产生其Enriques商的数量。我们通过晶格理论论证来谴责，超大的K3表面总是对小特征的领域具有综合商。对于某些小特征和一些Artin不变性，我们明确计算了超大型K3表面的Enriques商数量的下限。我们表明，在代数封闭的特征$ 3 $上，Artin不变的超高K3表面$ 1 $具有两个Enriques商。
We show that most classes of K3 surfaces have only finitely many Enriques quotients. For supersingular K3 surfaces over fields of characteristic $p \geq 3$, we give a formula which generically yields the number of their Enriques quotients. We reprove via a lattice theoretic argument that supersingular K3 surfaces always have an Enriques quotient over fields of small characteristic. For some small characteristics and some Artin invariants, we explicitly compute lower bounds for the number of Enriques quotients of a supersingular K3 surface. We show that the supersingular K3 surface of Artin invariant $1$ over an algebraically closed field of characteristic $3$ has exactly two Enriques quotients.
