{"paper":{"title":"On a connectedness principle of Shokurov-Koll\\'ar type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christopher D. Hacon, Jingjun Han","submitted_at":"2018-01-05T15:51:28Z","abstract_excerpt":"Let $(X,\\Delta)$ be a log pair over $S$, such that $-(K_X+\\Delta)$ is nef over $S$. It is conjectured that the intersection of the non-klt (non Kawamata log terminal) locus of $(X,\\Delta)$ with any fiber $X_s$ has at most two connected components. We prove this conjecture in dimension $\\leq 4$ and in arbitrary dimension assuming the termination of klt flips."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01801","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"}