{"paper":{"title":"Classification of toric manifolds over an $n$-cube with one vertex cut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AT","authors_text":"Hideya Kuwata, Mikiya Masuda, Seonjeong Park, Sho Hasui","submitted_at":"2017-05-22T01:26:00Z","abstract_excerpt":"We say that a complete nonsingular toric variety (called a toric manifold in this paper) is over $P$ if its quotient by the compact torus is homeomorphic to $P$ as a manifold with corners. Bott manifolds (or Bott towers) are toric manifolds over an $n$-cube $I^n$ and blowing them up at a fixed point produces toric manifolds over $\\mathrm{vc}(I^n)$ an $n$-cube with one vertex cut. They are all projective. On the other hand, Oda's $3$-fold, the simplest non-projective toric manifold, is over $\\mathrm{vc}(I^n)$. In this paper, we classify toric manifolds over $\\mathrm{vc}(I^n)$ $(n\\ge 3)$ as vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07530","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"}