{"paper":{"title":"The locus of points of the Hilbert scheme with bounded regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristina Bertone, Edoardo Ballico, Margherita Roggero","submitted_at":"2011-11-08T18:40:34Z","abstract_excerpt":"In this paper we consider the Hilbert scheme $Hilb_{p(t)}^n$ parameterizing subschemes of $P^n$ with Hilbert polynomial $p(t)$, and we investigate its locus containing points corresponding to schemes with regularity lower than or equal to a fixed integer $r'$. This locus is an open subscheme of $Hilb_{p(t)}^n$ and, for every $s\\geq r'$, we describe it as a locally closed subscheme of the Grasmannian $Gr_{p(s)}^{N(s)}$ given by a set of equations of degree $\\leq \\mathrm{deg}(p(t))+2$ and linear inequalities in the coordinates of the Pl\\\"ucker embedding."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2007","kind":"arxiv","version":3},"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"}