{"paper":{"title":"Multi-Rees Algebras of Strongly Stable Ideals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Gabriel Sosa, Kuei-Nuan Lin, Selvi Kara","submitted_at":"2020-12-31T04:46:05Z","abstract_excerpt":"We prove that the multi-Rees algebra $\\mathcal{R}(I_1 \\oplus \\cdots \\oplus I_r)$ of a collection of strongly stable ideals $I_1, \\ldots, I_r$ is of fiber type. In particular, we provide a Gr\\\"obner basis for its defining ideal as a union of a Gr\\\"obner basis for its special fiber and binomial syzygies. We also study the Koszulness of $\\mathcal{R}(I_1 \\oplus \\cdots \\oplus I_r)$ based on parameters associated to the collection. Furthermore, we establish a quadratic Gr\\\"obner basis of the defining ideal of $\\mathcal{R}(I_1 \\oplus I_2)$ where each of the strongly stable ideals has two quadric Bore"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.15447","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.15447/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}