{
  "abstract": "Let $L\\subseteq\\mathbb Z^4$ be a rank-three lattice possessing an admissible basis, and let $S=K[x_1,\\ldots,x_4]$ be the polynomial ring over a field $K$. We show that the associated lattice ideal $I_L \\subset S$ is generic and that $S/I_L$ is a Cohen--Macaulay ring. We also identify the neighbors of the origin in $L$ and the indispensable binomials of $I_L$. Moreover, we prove that the Betti numbers of $S/I_L$ are $β_0(S/I_L)=1$, $β_1(S/I_L)=7$, $β_2(S/I_L)=12$, and $β_3(S/I_L)=6$. In addition, we show that $I_L$ is a set-theoretic complete intersection over an arbitrary field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.18697",
  "author_total": 1,
  "authors": [
    {
      "name": "Anargyros Katsabekis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aw50mt2pmx6vd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.18697",
  "fulltext_url": null,
  "id": "aw50mt2pmx6vd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.18697",
  "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": "W7170034542",
  "pdf_url": "https://arxiv.org/pdf/2607.18697",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aw50mt2pmx6vd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2607.18697",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.18697"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Admissible bases and generic lattice ideals",
  "title_text": "Admissible bases and generic lattice ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/aw50mt2pmx6vd",
  "venue": "arXiv",
  "versions": []
}