Computing isogenies from modular equations in genus two
Résumé
We present an algorithm solving the following problem: given two
genus 2 curves over a field k with isogenous Jacobians, compute
such an isogeny explicitly. This isogeny can be either an
l-isogeny or, in the real multiplication case, an isogeny with
cyclic kernel; we require that k have large enough characteristic
and that the curves be sufficiently generic. Our algorithm uses
modular equations for these isogeny types, and makes essential use
of an explicit Kodaira--Spencer isomorphism in genus 2.
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