{"paper":{"title":"Schottky via the punctual Hilbert scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mart\\'i Lahoz, Martin G. Gulbrandsen","submitted_at":"2014-10-17T18:21:17Z","abstract_excerpt":"We show that a smooth projective curve of genus $g$ can be reconstructed from its polarized Jacobian $(X, \\Theta)$ as a certain locus in the Hilbert scheme $\\mathrm{Hilb}^d(X)$, for $d=3$ and for $d=g+2$, defined by geometric conditions in terms of the polarization $\\Theta$. The result is an application of the Gunning--Welters trisecant criterion and the Castelnuovo--Schottky theorem by Pareschi--Popa and Grushevsky, and its scheme theoretic extension by the authors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4813","kind":"arxiv","version":1},"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"}