{"paper":{"title":"On the Hilbert scheme of a Prym variety","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Sernesi, Herbert Lange","submitted_at":"2002-06-24T11:32:33Z","abstract_excerpt":"To any unramified double cover $\\pi:\\tilde C \\to C$ of projective irreducible and nonsingular curves one associates the Prym variety $P = P(\\pi)$. For $C$ nonhyperelliptic of genus $g \\geq 6$ we consider the natural embedding $\\tilde C \\subset P$ (defined up to translation) of $\\tilde C$ into $P$ and we study the local structure of the Hilbert scheme $Hilb^P$ of $P$ at the point\n $[\\tilde C]$. We show that this structure is related with the local geometry of the Prym map, or more precisely with the validity of the infinitesimal version of Torelli's theorem for Pryms at $[\\pi]$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0206248","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"}