{"paper":{"title":"On the connectedness principle and dual complexes for generalized pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Roberto Svaldi, Stefano Filipazzi","submitted_at":"2020-10-15T20:55:56Z","abstract_excerpt":"Let $(X,B)$ be a pair, and let $f \\colon X \\rightarrow S$ be a contraction with $-(K_X + B)$ nef over $S$. A conjecture, known as the Shokurov-Koll\\'{a}r connectedness principle, predicts that $f^{-1} (s) \\cap \\mathrm{Nklt}(X,B)$ has at most two connected components, where $s \\in S$ is an arbitrary schematic point and $\\mathrm{Nklt}(X,B)$ denotes the non-klt locus of $(X,B)$. In this work, we prove this conjecture, characterizing those cases in which $\\mathrm{Nklt}(X,B)$ fails to be connected, and we extend these same results also to the category of generalized pairs. Finally, we apply these r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.08018","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.08018/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}