The Scorza correspondence in genus 3 |
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Authors: | Samuel Grushevsky Riccardo Salvati Manni |
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Institution: | 1. Mathematics Department, Stony Brook University, Stony Brook, NY, 11790-3651, USA 2. Dipartimento di Matematica, Università “La Sapienza”, Piazzale A. Moro 2, 00185, Roma, Italy
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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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