论文标题
关于K3表面的广义弗朗切塔猜想的评论
A remark on the generalized Franchetta conjecture for K3 surfaces
论文作者
论文摘要
如果通用纤维上的0-Cycles的Chow组是循环的，则K3表面$ \ Mathscr {x} \ rightArrow b $具有\ emph {franchetta属性}。奥格雷迪（O'Grady）提出的广泛的弗朗切塔（Franchetta）猜想断言，通用家族$ \ mathscr {x} _g \ rightarrow \ rightarrow \ Mathscr {f} _g $ of 2g-2 $ of 2g-2 $的二极化k3 _g $具有Franchetta财产。虽然这仅以小$ g $而闻名。
A family of K3 surfaces $\mathscr{X}\rightarrow B$ has the \emph{Franchetta property} if the Chow group of 0-cycles on the generic fiber is cyclic. The generalized Franchetta conjecture proposed by O'Grady asserts that the universal family $\mathscr{X}_g\rightarrow \mathscr{F}_g$ of polarized K3 of degree $2g-2$ has the Franchetta property. While this is known only for small $g$ thanks to \cite{PSY}, we prove that for all $g$ there is a hypersurface in $ \mathscr{F}_g$ such that the corresponding family has the Franchetta property.
