{"paper":{"title":"A property deducible from the generic initial ideal","license":"","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"alg-geom","authors_text":"Gunnar Floystad","submitted_at":"1997-08-22T14:19:15Z","abstract_excerpt":"Let $S_d$ be the vector space of monomials of degree $d$ in the variables $x_1, ..., x_s$. For a subspace $V \\sus S_d$ which is in general coordinates, consider the subspace $\\gin V \\sus S_d$ generated by initial monomials of polynomials in $V$ for the revlex order. We address the question of what properties of $V$ may be deduced from $\\gin V$. % This is an approach for understanding what algebraic or geometric properties of a homogeneous ideal $I \\sus k[x_1, ..., x_s]$ that may be deduced from its generic initial ideal $\\gin I$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9708020","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"}