Manuscripta Mathematica

, Volume 141, Issue 1–2, pp 111–124 | Cite as

The Scorza correspondence in genus 3

Article

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 \({\{x, \sigma(x) \mid x \in C\}}\) (where σ is the hyperelliptic involution), and twice the diagonal. Our proof uses the geometry of the subsystem Γ00 of the linear system |2Θ|, and Riemann identities for theta constants.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Mathematics DepartmentStony Brook UniversityStony BrookUSA
  2. 2.Dipartimento di MatematicaUniversità “La Sapienza”RomaItaly

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