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

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Referenced Papers

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Showing 1-4 of 4 references

Prym varieties and the geodesic flow on SO ( n )

  • Pan S. Pantazis
  • Math . Ann .
  • 1974

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

  • Cox D. A. Cox, R. Don

Theta characteristics on an algebraic curve

  • D. Mumford
  • J . de Math .

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