{"paper":{"title":"On factorizations of maps between curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dijana Kreso, Michael E. Zieve","submitted_at":"2014-05-19T14:45:38Z","abstract_excerpt":"We examine the different ways of writing a cover of curves $\\phi\\colon C\\to D$ over a field $K$ as a composition $\\phi=\\phi_n\\circ\\phi_{n-1}\\circ\\dots\\circ\\phi_1$, where each $\\phi_i$ is a cover of curves over $K$ of degree at least $2$ which cannot be written as the composition of two lower-degree covers. We show that if the monodromy group $\\textrm{Mon}(\\phi)$ has a transitive abelian subgroup then the sequence $(\\deg\\phi_i)_{1\\le i\\le n}$ is uniquely determined up to permutation by $\\phi$, so in particular the length $n$ is uniquely determined. We prove analogous conclusions for the sequenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4753","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"}