{"paper":{"title":"Associated points and integral closure of modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Antoni Rangachev","submitted_at":"2016-11-11T23:34:35Z","abstract_excerpt":"Let $X:=\\mathrm{Spec}(R)$ be an affine Noetherian scheme, and $\\mathcal{M} \\subset \\mathcal{N}$ be a pair of finitely generated $R$-modules. Denote their Rees algebras by $\\mathcal{R}(\\mathcal{M})$ and $\\mathcal{R}(\\mathcal{N})$. Let $\\mathcal{N}^{n}$ be the $n$th homogeneous component of $\\mathcal{R}(\\mathcal{N})$ and let $\\mathcal{M}^{n}$ be the image of the $n$th homegeneous component of $\\mathcal{R}(\\mathcal{M})$ in $\\mathcal{N}^n$. Denote by $\\overline{\\mathcal{M}^{n}}$ be the integral closure of $\\mathcal{M}^{n}$ in $\\mathcal{N}^{n}$. We prove that $\\mathrm{Ass}_{X}(\\mathcal{N}^{n}/\\over"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03910","kind":"arxiv","version":3},"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"}