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

@article{Hanselman2020GluingCO, title={Gluing curves of genus 1 and 2 along their 2-torsion.}, author={Jeroen Hanselman and Sam Schiavone and Jeroen Sijsling}, journal={arXiv: Algebraic Geometry}, year={2020} }

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 Jacobian is up to twist (2,2,2)-isogenous to the products of the Jacobians of $X$ and $Y$. Moreover, we give algorithms to construct the curve $Z$ once equations for $X$ and $Y$ are given. The first of these involves the use of hyperplane sections of the Kummer variety of $Y$ whose desingularization is isomorphic to $X… CONTINUE READING

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