{"paper":{"title":"Galois points for a normal hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Satoru Fukasawa, Takeshi Takahashi","submitted_at":"2009-07-28T04:46:37Z","abstract_excerpt":"We study Galois points for a hypersurface $X$ with $\\dim {\\rm Sing}(X) \\le \\dim X-2$. The purpose of this article is to determine the set $\\Delta(X)$ of Galois points in characteristic zero: Indeed, we give a sharp upper bound of the number of Galois points in terms of $\\dim X$ and $\\dim {\\rm Sing}(X)$ if $\\Delta(X)$ is a finite set, and prove that $X$ is a cone if $\\Delta(X)$ is infinite. To achieve our purpose, we need a certain hyperplane section theorem on Galois point. We prove this theorem in arbitrary characteristic. On the other hand, the hyperplane section theorem has other important "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4834","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"}