{"paper":{"title":"Local Fano-Mori contractions of high nef-value","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Tasin, Marco Andreatta","submitted_at":"2014-05-21T10:02:14Z","abstract_excerpt":"Let $X$ be a variety with at most terminal $\\mathbb Q$-factorial singularities of dimension $n$. We study local contractions $f:X\\to Z$ supported by a $\\mathbb Q$-Cartier divisor of the type $K_X+ \\tau L$, where $L$ is an $f$-ample Cartier divisor and $\\tau \\geq 0$ is a rational number. Equivalently, $f$ is a Fano-Mori contraction associated to an extremal face in $\\overline {NE(X)}_{K_X+\\tau L = 0}$; these maps naturally arise in the context of the minimal model program. We prove that, if $\\tau > (n-3) >0$, the general element $X' \\in |L|$ is a variety with at most terminal singularities. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5353","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"}