Mathematics – Algebraic Geometry
Scientific paper
2011-02-09
Mathematics
Algebraic Geometry
13 pages; typos corrected, minor changes
Scientific paper
We prove that there exists a number field $K$ and a smooth $\mathrm{K3}$
surface $S_{22}$ over $K$ such that the geometric Picard number of $S_{22}$
equals 1, $S_{22}$ is of genus 12, and the set of $K$-points is Zariski dense
in $S_{22}$.
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