论文标题
K3表面的杰出家庭：扭曲空间，Brauer团体和Noether-Lefschetz Loci
Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether-Lefschetz loci
论文作者
论文摘要
我们描述了K3表面的杰出家族的霍奇理论。它们的特征是在Noether-Lefschetz基因座中的任何两个纤维的Hodge结构之间的紧密联系。该理论涵盖了扭曲物变形，分析性泰特 - 毛病组和一维Shimura特殊周期。在这种情况下，Brauer群体被视为Brauer家族的Noether-Lefschetz基因座，或者是Noether-Lefschetz基因座的专业化，在一个接近扭曲的空间中。从一个代数扭曲的纤维传递到另一个代数扭曲的纤维，通过构造是先验操作，在这里被视为首先沿着更代数的brauer家族，然后沿一个代数K3表面的家族变形。
We describe the Hodge theory of brilliant families of K3 surfaces. Their characteristic feature is a close link between the Hodge structures of any two fibres over points in the Noether-Lefschetz locus. Twistor deformations, the analytic Tate-Safarevic group, and one-dimensional Shimura special cycles are covered by the theory. In this setting, the Brauer group is viewed as the Noether-Lefschetz locus of the Brauer family or as the specialization of the Noether-Lefschetz loci in a family of approaching twistor spaces. Passing from one algebraic twistor fibre to another, which by construction is a transcendental operation, is here viewed as first deforming along the more algebraic Brauer family and then along a family of algebraic K3 surfaces.
