论文标题
具有实际乘法的$ k3 $表面的显式家庭
Explicit families of $K3$ surfaces having real multiplication
论文作者
论文摘要
对于$ k3 $表面的家庭，我们为真实或复杂的乘法建立了足够的标准。我们的标准本质上是算术的。最初，这可能表明该家族的通用纤维具有非平凡的内态领域。此外，内态领域在专业方面不会缩小。作为一个应用程序，我们分别介绍了两个具有$ \ bbq（\ sqrt {2}）$和$ \ bbq（\ sqrt {5}）$的$ k3 $表面的显式家庭。
For families of $K3$ surfaces, we establish a sufficient criterion for real or complex multiplication. Our criterion is arithmetic in nature. It may show, at first, that the generic fibre of the family has a nontrivial endomorphism field. Moreover, the endomorphism field does not shrink under specialisation. As an application, we present two explicit families of $K3$ surfaces having real multiplication by $\bbQ(\sqrt{2})$ and $\bbQ(\sqrt{5})$, respectively.
