{"paper":{"title":"The Scorza correspondence in genus 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Riccardo Salvati Manni, Samuel Grushevsky","submitted_at":"2010-09-02T10:14:48Z","abstract_excerpt":"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 a hyperelliptic genus 3 curve C is the union of the curve ${x,\\sigma(x))$ (where $\\sigma$ is the hyperelliptic involution), and twice the diagonal. Our proof uses the geometry of the subsystem \\Gamma_{00} of the linear system 2\\Theta, and Riemann identities for theta constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0375","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}