{"paper":{"title":"Infinitesimal extensions of rank two vector bundles on submanifolds of small codimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lucian Badescu","submitted_at":"2014-12-15T20:08:19Z","abstract_excerpt":"Let $X$ be a submanifold of dimension $n$ of the complex projective space $\\mathbb P^N$ ($n<N$), and let $E$ be a vector bundle of rank two on $X$ . If $n\\geq\\frac{N+3}{2}\\geq 4$ we prove a geometric criterion for the existence of an extension of $E$ to a vector bundle on the first order infinitesimal neighborhood of $X$ in $\\mathbb P^N$ in terms of the splitting of the normal bundle sequence of $Y\\subset X\\subset\\mathbb P^N$, where $Y$ is the zero locus of a general section of a high twist of $E$. In the last section we show that the universal quotient vector bundle on the Grassmann variety $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4746","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"}