{"paper":{"title":"Plane algebraic curves in fancy balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"N. G. Kruzhilin, S. Yu. Orevkov","submitted_at":"2020-06-30T20:32:51Z","abstract_excerpt":"Boileau and Rudolph called a link $L$ in the $3$-sphere a $\\bf C$-boundary if it can be realized as the intersection of an algebraic curve $A$ in $\\bf C^2$ with the boundary of a smooth embedded $4$-ball $B$. They showed that some links are not $\\bf C$-boundaries. We say that $L$ is a strong $\\bf C$-boundary if $A\\setminus B$ is connected. In particular, all quasipositive links are strong $\\bf C$-boundaries. In this paper we give examples of non-quasipositive strong $\\bf C$-boundaries and non-strong $\\bf C$-boundaries. We give a complete classification of (strong) $\\bf C$-boundaries with at mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.00098","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.00098/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"}