{"paper":{"title":"Diagonal Subalgebras of Residual Intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"H. Ananthnarayan, Neeraj Kumar, Vivek Mukundan","submitted_at":"2019-01-15T19:44:52Z","abstract_excerpt":"Let ${\\sf k}$ be a field, $S$ be a bigraded ${\\sf k}$-algebra, and $S_\\Delta$ denote the diagonal subalgebra of $S$ corresponding to $\\Delta = \\{ (cs,es) \\; | \\; s \\in \\mathbb{Z} \\}$. It is know that the $S_\\Delta$ is Koszul for $c,e \\gg 0$. In this article, we find bounds for $c,e$ for $S_\\Delta$ to be Koszul, when $S$ is a geometric residual intersection. Furthermore, we also study the Cohen-Macaulay property of these algebras. Finally, as an application, we look at classes of linearly presented perfect ideals of height two in a polynomial ring, show that all their powers have a linear resol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05027","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":""},"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"}