{"paper":{"title":"Injectivity on one line","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Janusz Gwo\\'zdziewicz","submitted_at":"1993-05-19T07:43:35Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic zero. Let $H:k^2\\to k^2$ be a polynomial mapping such that the Jacobian $\\text{Jac}\\,H$ is a non-zero constant. In this note we prove, that if there is a line $l \\subset k^2$ such that $H|_l:l\\to k^2$ is an injection, then $H$ is a polynomial automorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9305008","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"}