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

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

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