The Arithmetic-geometric Mean and Isogenies for Curves of Higher Genus

@inproceedings{Donagi1997TheAM,
title={The Arithmetic-geometric Mean and Isogenies for Curves of Higher Genus},
author={Ron Donagi and Ron Livne},
year={1997}
}

Computation of Gauss's arithmetic-geometric mean involves iteration of a simple step, whose algebro-geometric interpretation is the construction of an elliptic curve isogenous to a given one, specifically one whose period is double the original period. A higher genus analogue should involve the explicit construction of a curve whose jacobian is isogenous to the jacobian of a given curve. The doubling of the period matrix means that the kernel of the isogeny should be a lagrangian subgroup of… CONTINUE READING

Donagi , The fibers of the Prym map , in Curves , Jacobians , and Abelian Varieties , Proceedings of an AMSIMSSIAM Joint Summer Research Conference on the Schottky Problems