{"paper":{"title":"The Variety of Polar Simplices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Frank-Olaf Schreyer, Kristian Ranestad","submitted_at":"2011-04-14T11:23:59Z","abstract_excerpt":"A collection of n distinct hyperplanes L_i ={l_i=0} in P^{n-1}, the n-1-dimensional projective space over an algebraically closed field of characteristic not equal to 2, is a polar simplex of a quadric Q={q=0}, if each L_i is the polar hyperplane of the point p_i, the intersection point of the L_j with j different from i, equivalently, if q= l_1^2+...+l_n^2 for suitable choices of the linear forms l_i. In this paper we study the closure VPS(Q,n) in Hilb_n(P^{n-1}) of the variety of sums of powers presenting Q from a global viewpoint: VPS(Q,n) is a smooth Fano variety of index 2 and Picard numb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2728","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"}