{"paper":{"title":"Effective Adjunction Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claudio Fontanari, Marco Andreatta","submitted_at":"2017-03-02T12:29:10Z","abstract_excerpt":"Here we investigate the property of effectivity for adjoint divisors. Among others, we prove the following results:\n  (i) A normal projective variety $X$ with at most canonical singularities is uniruled if and only if for each very ample Cartier divisor $H$ on $X$ we have $H^0(X, m_0K_X+H)=0$ for some $m_0=m_0(H)>0$.\n  (ii) Let $(X,L)$ be a polarized manifold of dimension $4$ and let $t$ be an integer with $t \\ge 3$. If $K_X+tL$ is pseudo-effective, then $H^0(X, K_X+tL) \\ne 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00758","kind":"arxiv","version":4},"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"}