{
  "abstract": "Let $S=k[x_1,\\ldots,x_n]$ and let $I=I_Δ\\subsetneq S$ be a nonzero squarefree monomial ideal. Motivated by the classical higher-order Kähler differential modules and by the theory of higher conormal modules, we study not only the higher conormal quotients $I/I^q$, but more generally the shifted quotients $I^r/I^q$, $1\\le r<q$, in the same $I$-adic conormal filtration, together with their symbolic analogues $I^{(r)}/I^{(q)}$. We prove that, for every $1\\le r<q$ with $q\\ge3$, the module $I^r/I^q$ is Cohen--Macaulay if and only if $I$ is a complete intersection. In sharp contrast, $I^{(r)}/I^{(q)}$ is Cohen--Macaulay if and only if $Δ$ is a matroid, where loops are allowed. Thus, the Cohen--Macaulayness of a single nonexceptional window forces the Cohen--Macaulayness of every window in the corresponding filtration. The unique exceptional pair is $(r,q)=(1,2)$: at this conormal level, we show that the Cohen--Macaulayness of $I/I^2$ forces $I^2=I^{(2)}$, and hence $I/I^{(2)}$ is Cohen--Macaulay.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18071",
  "author_total": 2,
  "authors": [
    {
      "name": "Tài Huy Hà"
    },
    {
      "name": "Nguyen Cong Minh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f5xpc3ncet0pa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18071",
  "fulltext_url": null,
  "id": "f5xpc3ncet0pa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18071",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7213505359",
  "pdf_url": "https://arxiv.org/pdf/2609.18071",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f5xpc3ncet0pa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18071",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18071"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Cohen-Macaulay higher conormal and Kähler differential modules of squarefree monomial ideals",
  "title_text": "Cohen-Macaulay higher conormal and Kähler differential modules of squarefree monomial ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/f5xpc3ncet0pa",
  "venue": "arXiv",
  "versions": []
}