# The Scorza correspondence in genus 3 - Mathematics > Algebraic Geometry

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Abstract: In this note we prove the genus 3 case of a conjecture of G. Farkas and A.Verra on the limit of the Scorza correspondence for curves with a theta-null.Specifically, we show that the limit of the Scorza correspondence for ahyperelliptic genus 3 curve C is the union of the curve ${x,\sigmax$ where$\sigma$ is the hyperelliptic involution, and twice the diagonal. Our proofuses the geometry of the subsystem \Gamma {00} of the linear system 2\Theta,and Riemann identities for theta constants.

Autor: Samuel Grushevsky, Riccardo Salvati Manni

Fuente: https://arxiv.org/