{"paper":{"title":"Varieties of minimal rational tangents on double covers of projective space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hosung Kim, Jun-Muk Hwang","submitted_at":"2013-03-29T07:03:23Z","abstract_excerpt":"Let $\\phi: X \\to \\mathbb P^n$ be a double cover branched along a smooth hypersurface of degree $2m, 2 \\leq m \\leq n-1$. We study the varieties of minimal rational tangents $\\mathcal C_x \\subset \\mathbb P T_x(X)$ at a general point $x$ of $X$. We describe the homogeneous ideal of $\\mathcal C_x$ and show that the projective isomorphism type of $\\mathcal C_x$ varies in a maximal way as $x$ varies over general points of $X$. Our description of the ideal of $\\mathbb C_x$ implies a certain rigidity property of the covering morphism $\\phi$. As an application of this rigidity, we show that any finite "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7312","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"}