An explicit formula for the genus 3 AGM

2001/11/27 by D. Lehavi, Lehavi, D.
Mathematics · #14H40 #14H45 #14Q05 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H40 #msc:14H45 #msc:14Q05

paper · pdf · doi:10.48550/arxiv.math/0111273

13 pages, LaTeX 2e amsart, xypic. New version includes explicit identification of the differentials

arxiv created 2002/11/21 · arxiv updated 2009/11/30

Abstract

Given a smooth non-hyperelliptic curve C of genus 3 and a maximal isotropic subgroup (w.r.t. the Weil pairing) L in Jac(C)[2], there exists a smooth curve C' s.t. Jac(C')=Jac(C)/L. This construction is symmetric. i.e. if we start with C' and the dual flag on it, we get C. A previous less explicit approach was taken by Donagi and Livne. The advantage of our construction is that it is explicit enough to describe the isomorphism H⁰(C,K_C)=H⁰(C',K_C').

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