{
  "abstract": "Let $G$ be a finite simple graph on $[n]$ and let $I_c(G)$ denote its complementary edge ideal in the polynomial ring $S = K[x_1,\\dots,x_n]$. We give a combinatorial description, in terms of the structure of $G$, of the minimal generators of the symbolic Rees algebra $\\mathcal{R}_s(I_c(G)) = \\bigoplus_{k \\geq 0} I_c(G)^{(k)} t^k$, and show that this algebra is generated in degree at most $6$. Moreover, we completely determine the minimal generators of $\\mathcal{R}_{s}(I_{c}(G))$ in graph-theoretic terms. We then study in more detail the homological invariants of the symbolic powers $I_c(G)^{(k)}$ for the classes of cycle graphs and complete multipartite graphs. For theses families, we study the behavior of the symbolic depth function $k\\mapsto\\operatorname{depth} S/I_c(G)^{(k)}$, we obtain the limit depth of the symbolic powers and the Waldschmidt constant of $I_c(G)$, and further prove that all the symbolic powers $I_c(G)^{(k)}$ are componentwise linear.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01165",
  "author_total": 3,
  "authors": [
    {
      "name": "Antonino Ficarra"
    },
    {
      "name": "Somayeh Moradi"
    },
    {
      "name": "Yuji Muta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9fhjp4zxv2zs8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01165",
  "fulltext_url": null,
  "id": "9fhjp4zxv2zs8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01165",
  "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": "W7206193609",
  "pdf_url": "https://arxiv.org/pdf/2609.01165",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9fhjp4zxv2zs8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.01165",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01165"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Symbolic Rees algebras of complementary edge ideals",
  "title_text": "Symbolic Rees algebras of complementary edge ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/9fhjp4zxv2zs8",
  "venue": "arXiv",
  "versions": []
}