{"paper":{"title":"Tower sets and other configurations with the Cohen-Macaulay property","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alfio Ragusa, Giuseppe Favacchio, Giuseppe Zappal\\`a","submitted_at":"2014-01-15T10:18:38Z","abstract_excerpt":"Some well-known arithmetically Cohen-Macaulay configurations of linear varieties in $\\mathbb{P}^r$ as $k$-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are finite union of linear varieties whose support set is a suitable finite subset of $\\mathbb{Z}_+^c$ called tower set. We prove that the tower schemes are arithmetically Cohen-Macaulay and we compute their Hilbert function in terms of their support.\n  Afterwards, since even in codimension 2 not every arithmetically Cohen-Macaulay squarefree mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3535","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"}