Gluing curves of genus 1 and 2 along their 2-torsion

Jeroen Hanselman, Sam Schiavone, Jeroen Sijsling

Let $X$ (resp. $Y$) be a curve of genus 1 (resp. 2) over a base field $k$ whose characteristic does not equal 2. We give criteria for the existence of a curve $Z$ over $k$ whose Ja…