{
  "abstract": "Let $Δ_{m,n}$ be the chessboard complex, and let $J_{m,n}$ be the Stanley-Reisner ideal of its Alexander dual. We study the symbolic and ordinary powers of $J_{m,n}$, focusing on their homological and algebraic invariants. First, we characterize when $J_{m,n}^{(q)}$ has linear quotients. For the ordinary powers, we give sufficient conditions on $m$ and $n$ for $J_{m,n}^q$ to have linear quotients. We determine the maximal degree of a minimal generator and the Castelnuovo-Mumford regularity of $J_{m,n}^{(q)}$, obtaining explicit formulas for all $q\\ge2$ and showing that both invariants have the same asymptotic slope. We also compute the initial degrees and Waldschmidt constant, proving that $α(J_{m,n}^{(q)})$ is a degree-one quasi-polynomial of period two and $\\widehatα(J_{m,n})=mn/2$. Explicit formulas for the $\\mathrm{v}$-numbers of symbolic and ordinary powers are obtained. Finally, for every $m\\ge3$, we show that $J_{m,2m-1}$ is not weakly polymatroidal, disproving a conjecture of Lu and Wang in this setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37219",
  "author_total": 2,
  "authors": [
    {
      "name": "Arka Ghosh"
    },
    {
      "name": "S. Selvaraja"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1nz9vbxdky1ad.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37219",
  "fulltext_url": null,
  "id": "1nz9vbxdky1ad",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37219",
  "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"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7214981733",
  "pdf_url": "https://arxiv.org/pdf/2609.37219",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1nz9vbxdky1ad.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37219",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37219"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Powers of Alexander Duals of Stanley-Reisner Ideals of Chessboard Complexes",
  "title_text": "Powers of Alexander Duals of Stanley-Reisner Ideals of Chessboard Complexes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/1nz9vbxdky1ad",
  "venue": "arXiv",
  "versions": []
}