{"paper":{"title":"Characterizing Jacobians via flexes of the Kummer variety","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"E. Arbarello, G. Marini, I. Krichever","submitted_at":"2005-02-07T17:16:21Z","abstract_excerpt":"Given an abelian variety $X$ and a point $a\\in X$ we denote by $<a>$ the closure of the subgroup of $X$ generated by $a$. Let $N=2^g-1$. We denote by $\\kappa: X\\to \\kappa(X)\\subset\\mathbb P^N$ the map from $X$ to its Kummer variety. We prove that an indecomposable abelian variety $X$ is the Jacobian of a curve if and only if there exists a point $a=2b\\in X\\setminus\\{0\\}$ such that $<a>$ is irreducible and $\\kappa(b)$ is a flex of $\\kappa(X)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502138","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"}