{"paper":{"title":"Monomial projections of Veronese varieties: new results and conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Liena Colarte-G\\'omez, Lisa Nicklasson, Rosa M. Mir\\'o-Roig","submitted_at":"2023-03-16T18:02:58Z","abstract_excerpt":"In this paper, we consider the homogeneous coordinate rings $A(Y_{n,d}) \\cong \\mathbb{K}[\\Omega_{n,d}]$ of monomial projections $Y_{n,d}$ of Veronese varieties parameterized by subsets $\\Omega_{n,d}$ of monomials of degree $d$ in $n+1$ variables where: (1) $\\Omega_{n,d}$ contains all monomials supported in at most $s$ variables and, (2) $\\Omega_{n,d}$ is a set of monomial invariants of a finite diagonal abelian group $G \\subset GL(n+1,\\mathbb{K})$ of order $d$. Our goal is to study when $\\mathbb{K}[\\Omega_{n,d}]$ is a quadratic algebra and, if so, when $\\mathbb{K}[\\Omega_{n,d}]$ is Koszul or G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.09582","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.09582/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"}