Decomposed Richelot isogenies of Jacobian varieties of curves of genus 3

TL;DR

This paper characterizes when the Jacobian of a genus 3 curve over an algebraically closed field admits a decomposed Richelot isogeny, providing necessary and sufficient conditions and describing their structures.

Contribution

It offers a complete criterion for decomposed Richelot isogenies of Jacobians of genus 3 curves and details their structural properties.

Findings

Necessary and sufficient conditions for decomposed Richelot isogenies

Structural classification of such isogenies

Applicable over algebraically closed fields of characteristic p > 2

Abstract

For a nonsingular projective curve $C$ of genus 3 defined over an algebraically closed field of characteristic $p > 2$, we give a necessary and sufficient condition that the Jacobian variety $J(C)$ has a decomposed Richelot isogeny outgoing from it and we determine the structures of decomposed ones.