{
  "abstract": "Let $(A,\\mathfrak{m})$ be a Gorenstein local ring with $G(A)$ Cohen-Macaulay, and let $M$ be a Cohen-Macaulay $A$-module of finite projective dimension. In \\cite{Quasipure}, the authors proved that $e_1(M)\\geq \\binom{c+1}{2}$, where $c=\\operatorname{reg}G(A)$ and $e_i(M)$ is the $i$th Hilbert coefficient of $M$. We first show that this bound remains valid when $A$ is Cohen-Macaulay. We then study upper bounds for $e_2(M)$ when $e_1(M)=\\binom{c+1}{2}+i$ for $i=1,2$, and investigate the consequences of equality. In particular, we obtain depth properties and explicit descriptions of the $h$-polynomial of $G(M)$. Finally, we extend these results to strict complete intersection rings without assuming that $M$ has finite projective dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10295",
  "author_total": 1,
  "authors": [
    {
      "name": "Samarendra Sahoo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dxaqdt6jgjns7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10295",
  "fulltext_url": null,
  "id": "dxaqdt6jgjns7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10295",
  "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"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7212181436",
  "pdf_url": "https://arxiv.org/pdf/2609.10295",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dxaqdt6jgjns7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10295",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10295"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bounds on Hilbert coefficients of Cohen-Macaulay modules having finite projective dimension",
  "title_text": "Bounds on Hilbert coefficients of Cohen-Macaulay modules having finite projective dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/dxaqdt6jgjns7",
  "venue": "arXiv",
  "versions": []
}