{"paper":{"title":"On sections of elliptic fibrations","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Burak Ozbagci, Mustafa Korkmaz","submitted_at":"2006-04-24T19:46:23Z","abstract_excerpt":"We find a new relation among right-handed Dehn twists in the mapping class group of a $k$-holed torus for $4 \\leq k \\leq 9$. This relation induces an elliptic Lefschetz pencil structure on the four-manifold \\cp $#(9-k)$ \\cpb $ $ with $k$ base points and twelve singular fibers. By blowing up the base points we get an elliptic Lefschetz fibration on the complex elliptic surface $E(1)=$ \\cp $#9$ \\cpb $ \\to S^2$ with twelve singular fibers and $k$ disjoint sections. More importantly we can locate these $k$ sections in a Kirby diagram of the induced elliptic Lefschetz fibration. The $n$-th power of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604516","kind":"arxiv","version":1},"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"}