{"paper":{"title":"Log canonical pairs with boundaries containing ample divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Zhengyu Hu","submitted_at":"2017-12-19T21:23:21Z","abstract_excerpt":"Let $(X,\\Delta)$ be a projective log canonical pair such that $\\Delta \\geq A$ where $A \\geq 0$ is an ample $\\mathbb{R}$-divisor. We prove that either $(X,\\Delta)$ has a good minimal model or a Mori fibre space. Moreover, if $X$ is $\\mathbb{Q}$-factorial, then any Log Minimal Model Program on $K_X+\\Delta$ with scaling terminates. As an application we prove that a log Fano type variety $X$ with $\\mathbb{Q}$-factorial log canonical singularities is a Mori dream space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07219","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"}