{"paper":{"title":"The Minimal Free Resolution of A Star-Configuration in $\\mathbb{P}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Jung Pil Park, Yong-Su Shin","submitted_at":"2014-04-18T09:15:05Z","abstract_excerpt":"We find the minimal free resolution of the ideal of a star-configuration in $\\mathbb{P}^n$ of type $(r,s)$ defined by general forms in $R=\\Bbbk[x_0,x_1,\\dots,x_n]$. This generalises the results of \\cite{AS:1,GHM} from a specific value of $r=2$ to any value of $1\\le r\\le n$. Moreover, we show that any star-configuration in $\\mathbb{P}^n$ is arithmetically Cohen-Macaulay. As an application, we construct a few of graded Artinian rings, which have the weak Lefschetz property, using the sum of two ideals of star-configurations in $\\mathbb{P}^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4724","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"}