{"paper":{"title":"Fano-Mukai fourfolds of genus $10$ as compactifications of $\\mathbb{C}^4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mikhail Zaidenberg, Yuri Prokhorov","submitted_at":"2017-06-15T15:26:46Z","abstract_excerpt":"It is known that the moduli space of smooth Fano-Mukai fourfolds $V_{18}$ of genus $10$ has dimension one. We show that any such fourfold is a completion of $\\mathbb{C}^4$ in two different ways. Up to isomorphism, there is a unique fourfold $V_{18}^{\\mathrm s}$ acted upon by $\\operatorname{SL}_2(\\mathbb{C})$. The group $\\operatorname{Aut}(V_{18}^{\\mathrm s})$ is a semidirect product $\\operatorname{GL}_2(\\mathbb{C})\\rtimes(\\mathbb{Z}/2\\mathbb{Z})$. Furthermore, $V_{18}^{\\mathrm s}$ is a $\\operatorname{GL}_2(\\mathbb{C})$-equivariant completion of $\\mathbb{C}^4$, and as well of $\\operatorname{GL}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04926","kind":"arxiv","version":2},"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"}