{
  "abstract": "In this paper, we investigate the difference between ordinary and symbolic powers of edge ideals on the Castelnuovo-Mumford regularity and the depth. As a main theorem, we prove that the regularities of ordinary and symbolic powers coincide for edge ideals of simplicial graphs, as a partial result of Minh's conjecture. For the depth, we first show that, for each $k\\geq2$, the inequality $\\operatorname{depth} S/I^{(k)}\\geq\\operatorname{depth} S/I^{k}$ does not hold for squarefree monomial ideals in general. On the other hand, we prove that it holds for edge ideals when $k=2,3$. We also study the symbolic-ordinary discrepancy module $I(G)^{(k)}/I(G)^{k}$ of the edge ideal $I(G)$ of a graph $G$ and give a graph-theoretic formula for its Krull dimension in terms of induced odd cycles of $G$, thereby answering a question and a problem posed by Ha and Minh.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05945",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuji Muta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/amv8mqwty0tp6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05945",
  "fulltext_url": null,
  "id": "amv8mqwty0tp6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05945",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7212076284",
  "pdf_url": "https://arxiv.org/pdf/2609.05945",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/amv8mqwty0tp6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05945",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05945"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Comparisons between ordinary and symbolic powers of edge ideals with respect to regularity and depth",
  "title_text": "Comparisons between ordinary and symbolic powers of edge ideals with respect to regularity and depth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/amv8mqwty0tp6",
  "venue": "arXiv",
  "versions": []
}