{"paper":{"title":"Rational components of Hilbert schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Margherita Roggero, Paolo Lella","submitted_at":"2009-03-05T16:45:51Z","abstract_excerpt":"The Gr\\\"obner stratum of a monomial ideal $\\id{j}$ is an affine variety that parametrizes the family of all ideals having $\\id{j}$ as initial ideal (with respect to a fixed term ordering). The Gr\\\"obner strata can be equipped in a natural way of a structure of homogeneous variety and are in a close connection with Hilbert schemes of subvarieties in the projective space $\\PP^n$. Using properties of the Gr\\\"obner strata we prove some sufficient conditions for the rationality of components of $\\hilb_{p(z)}^n$. We show for instance that all the smooth, irreducible components in $\\hilb_{p(z)}^n$ (o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1029","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"}