{"paper":{"title":"Smoothable Gorenstein points via marked schemes and double-generic initial ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristina Bertone, Francesca Cioffi, Margherita Roggero","submitted_at":"2017-12-18T13:38:09Z","abstract_excerpt":"Over an infinite field $K$ with $\\mathrm{char}(K)\\neq 2,3$, we investigate smoothable Gorenstein $K$-points in a punctual Hilbert scheme from a new point of view, which is based on properties of double-generic initial ideals and of marked schemes. We obtain the following results: (i) points defined by graded Gorenstein $K$-algebras with Hilbert function $(1,7,7,1)$ are smoothable, in the further hypothesis that $K$ is algebraically closed; (ii) the Hilbert scheme $\\mathrm{Hilb}_{16}^7$ has at least three irreducible components. The properties of marked schemes give us a simple method to comput"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06392","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"}