{"paper":{"title":"Generalized polarized manifolds with low second class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea Luigi Tironi, Antonio Lanteri","submitted_at":"2016-08-27T18:26:39Z","abstract_excerpt":"On a smooth complex projective variety $X$ of dimension $n$, consider an ample vector bundle $\\mathcal{E}$ of rank $r \\leq n-2$ and an ample line bundle $H$. A numerical character $m_2=m_2(X,\\mathcal{E},H)$ of the triplet $(X,\\mathcal{E},H)$ is defined, extending the well-known second class of a polarized manifold $(X,H)$, when either $n=2$ or $H$ is very ample. Under some additional assumptions on $\\mathcal{F}: = \\mathcal{E} \\oplus H^{\\oplus (n-r-2)}$, triplets $(X,\\mathcal{E},H)$ as above whose $m_2$ is small with respect to the invariants $d:=c_{n-2}(\\mathcal{F})H^2$ and $g:=1+\\frac{1}{2}\\b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07732","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"}