For products of two curves, the paper gives effective asymptotic thresholds for density of degree-d points and a nearly complete low-genus picture, with applications to abelian and bielliptic surfaces.
On (2,2)-decomposable genus 4 Jacobians
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Density of algebraic points on products of curves
For products of two curves, the paper gives effective asymptotic thresholds for density of degree-d points and a nearly complete low-genus picture, with applications to abelian and bielliptic surfaces.