For many one-punctured genus-2 curve families, a complex-analytically dense set of fibers has effectively computable integral points, proved via torsion density of sections of doubly elliptic schemes.
The B etti map associated to a section of an abelian scheme
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Examples of effectivity for integral points on certain curves of genus 2
For many one-punctured genus-2 curve families, a complex-analytically dense set of fibers has effectively computable integral points, proved via torsion density of sections of doubly elliptic schemes.