{"paper":{"title":"Some results on deformations of sections of vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abel Castorena, Gian Pietro Pirola","submitted_at":"2015-10-10T17:38:03Z","abstract_excerpt":"Let $E$ be a vector bundle on a smooth complex projective variety $X$. We study the family of sections $s_t\\in H^0(E\\otimes L_t)$ where $L_t\\in Pic^0(X)$ is a family of topologically trivial line bundle and $L_0=\\mathcal O_X,$ that is, we study deformations of $s=s_0$. By applying the approximation theorem of Artin [2] we give a transversality condition that generalizes the semi-regularity of an effective Cartier divisor. Moreover, we obtain another proof of the Severi-Kodaira-Spencer theorem [4]. We apply our results to give a lower bound to the continuous rank of a vector bundle as defined b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02964","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"}