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.
Then it follows by Theorem 4.3 and Lemma 4.5 that 2 ∈ δ(E′ 1 ×E2), and in fact there exists a quadratic extension L/k over which both rk E′ 1(L) > 0 and rk E2(L) > 0
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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.