{"paper":{"title":"Simplicity of some Jacobians with many automorphisms","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Ortega, G.P. Pirola, I. Spelta, J.C. Naranjo","submitted_at":"2024-11-15T12:14:04Z","abstract_excerpt":"We study an explicit $(2g-1)$-dimensional family of Jacobian varieties of dimension $\\frac{d-1}2(g-1)$, arising from quotient curves of unramified cyclic coverings of prime degree $d$ of hyperelliptic curves of genus $g\\ge 2$. By using a deformation argument, we prove that the generic element of the family is simple. Furthermore, we completely describe their endomorphism algebra, and we show that they admit a rank $\\frac{d-1}2-1$ group of non-polarized automorphisms. As an application of these results, we prove the generic injectivity of the Prym map for \\'etale cyclic coverings of hyperellipt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10134","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.10134/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}