{"paper":{"title":"On the smoothability of certain K\\\"ahler cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ronan J. Conlon","submitted_at":"2014-07-18T05:24:54Z","abstract_excerpt":"Let $D$ be a Fano manifold that may be realised as $\\mathbb{P}(\\mathcal{E})$ for some rank $2$ holomorphic vector bundle $\\mathcal{E}\\longrightarrow Z$ over some Fano manifold $Z$. Let $k\\in\\mathbb{N}$ divide $c_{1}(D)$. We classify those K\\\"ahler cones of dimension $\\leq4$ of the form $(\\frac{1}{k}K_{D})^{\\times}$ that are smoothable. As a consequence, we find that any irregular Calabi-Yau cone of dimension $\\leq 4$ of this form does not admit a smoothing, leaving $K_{\\mathbb{P}^{2}_{(2)}}^{\\times}$ as currently the only known example of a smoothable irregular Calabi-Yau cone in these dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4887","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"}