{"paper":{"title":"Finite translation orbits on double families of abelian varieties (with an appendix by E. Amerik)","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Ekaterina Amerik, Francesco Tropeano, Paolo Dolce","submitted_at":"2024-01-13T08:51:05Z","abstract_excerpt":"We study two families of $g$-dimensional abelian varieties, induced by distinct rational maps defined on a common variety $\\overline{\\mathcal A}$ and mapping to two bases $\\overline{S}_1$ and $\\overline{S}_2$. Two non-torsion sections induce birational fiberwise translations on $\\overline{\\mathcal A}$. We consider the action of a specific subset of the group generated by these translations. Under the assumption that $\\operatorname{dim} \\overline{S}_1 (= \\operatorname{dim} \\overline{S}_2) \\leq g$, we prove that the points with finite orbit are contained in a proper Zariski closed subset. This s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.07015","kind":"arxiv","version":5},"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/2401.07015/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"}