{"paper":{"title":"A Borel open cover of the Hilbert scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Cristina Bertone, Margherita Roggero, Paolo Lella","submitted_at":"2009-09-11T14:48:06Z","abstract_excerpt":"Let $p(t)$ be an admissible Hilbert polynomial in $\\PP^n$ of degree $d$. The Hilbert scheme $\\hilb^n_p(t)$ can be realized as a closed subscheme of a suitable Grassmannian $ \\mathbb G$, hence it could be globally defined by homogeneous equations in the Plucker coordinates of $ \\mathbb G$ and covered by open subsets given by the non-vanishing of a Plucker coordinate, each embedded as a closed subscheme of the affine space $A^D$, $D=\\dim(\\mathbb G)$. However, the number $E$ of Plucker coordinates is so large that effective computations in this setting are practically impossible. In this paper, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2184","kind":"arxiv","version":5},"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"}