In this note we prove the genus 3 case of a conjecture of Farkas and 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 a hyperelliptic genus 3 curve C is the union of the curve {x, σ(x) {pipe} x ∈ C} (where σ is the hyperelliptic involution), and twice the diagonal. Our proof uses the geometry of the subsystem Γ00 of the linear system {pipe}2Θ{pipe}, and Riemann identities for theta constants. © 2012 Springer-Verlag.
The Scorza correspondence in genus 3 / Samuel, Grushevsky; SALVATI MANNI, Riccardo. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - STAMPA. - 141:1-2(2013), pp. 111-124. [10.1007/s00229-012-0564-z]
The Scorza correspondence in genus 3
SALVATI MANNI, Riccardo
2013
Abstract
In this note we prove the genus 3 case of a conjecture of Farkas and 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 a hyperelliptic genus 3 curve C is the union of the curve {x, σ(x) {pipe} x ∈ C} (where σ is the hyperelliptic involution), and twice the diagonal. Our proof uses the geometry of the subsystem Γ00 of the linear system {pipe}2Θ{pipe}, and Riemann identities for theta constants. © 2012 Springer-Verlag.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
