Computing isogeny classes of typical principally polarized abelian surfaces over the rationals
To a curve of genus 2 over Q, one can associate a Jacobian. This Jacobian is an abelian surface and due to a theorem of Faltings we know that there only finitely many curves of genus 2 over Q up to isomorphism, whose Jacobian is isogenous to a given abelian surface. In this talk, I will explain a method to compute these finitely many curves in practice.
(Joint work with Shiva Chidambaram, Edgar Costa, and Jean Kieffer)