{"paper":{"title":"Are minimal degree rational curves determined by their tangent vectors?","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sandor J. Kovacs, Stefan Kebekus","submitted_at":"2002-06-19T07:25:23Z","abstract_excerpt":"Let X be a projective variety which is covered by rational curves, for instance a Fano manifold over the complex numbers. In this setup, characterization and classification problems lead to the natural question: \"Given two points on X, how many minimal degree rational curve are there which contain those points?\". A recent answer to this question led to a number of new results in classification theory. As an infinitesimal analogue, we ask \"How many minimal degree rational curves exist which contain a prescribed tangent vector?\"\n  In this paper, we give sufficient conditions which guarantee that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0206193","kind":"arxiv","version":2},"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"}