{"paper":{"title":"Quadratic embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Corrado Zanella, Hans Havlicek","submitted_at":"2012-10-07T13:31:06Z","abstract_excerpt":"The quadratic Veronese embedding $\\rho$ maps the point set $P$ of $\\PG{n,F)$ into the point set of $PG({n+2 \\choose 2}-1, F$ ($F$ a commutative field) and has the following well-known property: If $M\\subset P$, then the intersection of all quadrics containing $M$ is the inverse image of the linear closure of $M^{\\rho}$. In other words, $\\rho$ transforms the closure from quadratic into inear. In this paper we use this property to define \"quadratic embeddings\". We shall prove that if $\\nu$ is a quadratic embedding of $PG{n,F)$ into $PG(n',F')$ ($F$ a commutative field), then $\\rho^{-1}\\nu$ is di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2054","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"}