{"paper":{"title":"Relative Prym varieties associated to the double cover of an Enriques surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea Ferretti, Enrico Arbarello, Giulia Sacc\\`a","submitted_at":"2012-11-18T23:24:25Z","abstract_excerpt":"Given an Enriques surface $T$, its universal K3 cover $f: S\\to T$, and a genus $g$ linear system $|C|$ on $T$, we construct the relative Prym variety $P_H=\\Prym_{v, H}(\\D/\\CC)$, where $\\CC\\to |C|$ and $\\D\\to |f^*C|$ are the universal families, $v$ is the Mukai vector $(0,[D], 2-2g)$ and $H$ is a polarization on $S$. The relative Prym variety is a $(2g-2)$-dimensional possibly singular variety, whose smooth locus is endowed with a hyperk\\\"ahler structure. This variety is constructed as the closure of the fixed locus of a symplectic birational involution defined on the moduli space $M_{v,H}(S)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4268","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"}