Deligne-Mostow表和特殊曲面族
The Deligne-Mostow list and special families of surfaces
摘要：
我们研究是否存在无穷多个具有给定离散不变量的曲面，其H^2是CM型的。这是一个表面类似的猜想科尔曼曲线。我们构建了大量的例子家庭的表面与p_g = 1，在模空间切出一个特殊的子品种，这些提供了一个积极的回答我们的问题。其中大多数是家庭的K3曲面，但我们也得到了一些家庭的曲面的一般类型。作为我们建设的投入，我们使用德利涅和莫斯托的工作。最后，我们证明了一个非常一般的K3曲面不能被小亏格曲线的乘积所控制。
英文摘要：
We study whether there exist infinitely many surfaces with given discrete invariants for which the H^2 is of CM type. This is a surface analogue of a conjecture of Coleman about curves. We construct a large number of examples of families of surfaces with p_g = 1 that in the moduli space cut out a special subvariety; these provide a positive answer to our question. Most of these are families of K3 surfaces but we also obtain some families of surfaces of general type. As input for our construction we use the work of Deligne and Mostow. Finally we prove that a very general K3 surface cannot be dominated by a product of curves of small genus.
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。
