{"paper":{"title":"The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hisanori Ohashi, Shigeru Mukai","submitted_at":"2015-07-02T18:27:57Z","abstract_excerpt":"Let $S$ be the (minimal) Enriques surface obtained from the symmetric quartic surface $(\\sum_{i<j}x_ix_j)^2=kx_1x_2x_3x_4$ in $\\mathbb{P}^3$ with $k\\neq 0,4,36$, by taking quotient of the Cremona action $(x_i) \\mapsto (1/x_i)$. The automorphism group of $S$ is a semi-direct product of a free product $\\mathcal{F}$ of four involutions and the symmetric group $\\mathfrak{S}_4$. Up to action of $\\mathcal{F}$, there are exactly $29$ elliptic pencils on $S$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00682","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"}