{"paper":{"title":"On monodromy in families of elliptic curves over $\\mathbb C$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Serge Lvovski","submitted_at":"2017-05-05T08:46:10Z","abstract_excerpt":"We show that if we are given a smooth non-isotrivial family of elliptic curves over~$\\mathbb C$ with a smooth base~$B$ for which the general fiber of the mapping $J\\colon B\\to\\mathbb A^1$ (assigning $j$-invariant of the fiber to a point) is connected, then the monodromy group of the family (acting on $H^1(\\cdot,\\mathbb Z)$ of the fibers) coincides with $\\mathrm{SL}(2,\\mathbb Z)$; if the general fiber has $m\\ge2$ connected components, then the monodromy group has index at most~$2m$ in $\\mathrm{SL}(2,\\mathbb Z)$. By contrast, in \\emph{any} family of hyperelliptic curves of genus $g\\ge3$, the mon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02129","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":""},"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"}