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Paper 2017/006

Reduced Mumford divisors of a genus 2 curve through its jacobian function field

Eduardo Ruiz Duarte

Abstract

We explore the function field of the jacobian JH of a hyperelliptic curve H of genus 2 in order to find reduced coordinates to represent points of JH and do arithmetic. We show how this relates to the usual Mumford representation of points of JH. Moreover we identify the open subsets of JH where our reduced coordinates are defined, characterizing the elements which can be reduced and we discuss the group operation with them.

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Available format(s)
PDF
Publication info
Preprint. MINOR revision.
Keywords
hyperellipticMumfordarithmetic
Contact author(s)
e ruiz duarte @ rug nl
History
2017-01-11: received
Short URL
https://ia.cr/2017/006
License
Creative Commons Attribution
CC BY
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