{"paper":{"title":"Strata of vector spaces of forms in k[x,y] and of rational curves in P^k","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Anthony Iarrobino","submitted_at":"2013-06-06T02:03:00Z","abstract_excerpt":"Consider the polynomial ring R=k[x,y] over an infinite field k and the subspace R_j of degree-j homogeneous polynomials. The Grassmanian G=Grass (R_j,d) parametrizes the vector spaces V in R_j having dimension d. The strata Grass_H(R_j,d) in G determined by the Hilbert function H=H(R/(V)) or, equivalently, by the Betti numbers of the algebra R/(V), are locally closed and irreducible of known dimension. We had previously shown also that they satisfy a frontier property that the closure of a stratum is its union with lower strata [I1,I2]. Each stratum corresponds to a partition, and the the pose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1282","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"}