An analog of the Edwards model for Jacobians of genus 2 curves
arXiv:2211.01450 · doi:10.1007/s40993-024-00518-5
Abstract
We give the explicit equations for a P^3 x P^3 embedding of the Jacobian of a curve of genus 2, which gives a natural analog for abelian surfaces of the Edwards curve model of elliptic curves. This gives a much more succinct description of the Jacobian variety than the standard version in P^{15}. We also give a condition under which, as for the Edwards curve, the abelian surfaces have a universal group law.
42 pages, with two supplemental ancillary files of maple code. v3: extensive revisions, mainly to sections 2 and 5. In particular, section 2 was completely rewritten to use the language of algebraic theta functions; this resulted in a longer exposition