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arXiv · 2012.03332

A remark on the generalized Franchetta conjecture for K3 surfaces

Arnaud Beauville
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Abstract

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.

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Arnaud Beauville. 2020-12-06. A remark on the generalized Franchetta conjecture for K3 surfaces. https://arxiv.org/abs/2012.03332

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