{"paper":{"title":"Bilinkage in codimension $3$ and canonical surfaces of degree $18$ in $\\mathbb{P}^5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Grzegorz Kapustka, Michal Kapustka","submitted_at":"2013-12-10T15:01:08Z","abstract_excerpt":"We study the behavior of the bilinkage process in codimension $3$. In particular, we construct a smooth canonically embedded and linearly normal surface of general type of degree $18$ in $\\mathbb{P}^5$, this is probably the highest degree such surface may have. Next, we apply our construction to find a geometric description of Tonoli Calabi--Yau threefolds in $\\mathbb{P}^6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2824","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":""},"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"}