{
  "abstract": "A smooth complete intersection $X\\subset\\mathbb{P}^{n+2}_{\\mathbb{C}}$ of two quadrics admits an interpretation as a moduli space of bundles. For $n=2$, it parametrizes stable rank $2$ parabolic bundles on $\\mathbb{P}^1$ with five marked points, while for $n=3$ it parametrizes stable rank $2$ bundles of odd degree with fixed determinant on a genus $2$ curve. For general $n$, it can be interpreted as a moduli space of semistable twisted $\\mathrm{Spin}$-bundles. We study $X\\setminus W$, where $W$ is the wobbly locus, consisting of bundles that admit a nonzero nilpotent Higgs field. We prove that $W$ is an irreducible divisor for $n\\geq 3$ and compute $H_1(X\\setminus W,\\mathbb{Z})$. Using a root-stack description, we identify $π_1(X\\setminus W)$ with the kernel of a monodromy homomorphism from an orbifold mixed braid group. The Reidemeister-Schreier method then yields an explicit presentation in every dimension. For $n=2$, where $X$ is a degree $4$ del Pezzo surface and $W$ is the union of its sixteen $(-1)$-curves, we obtain a presentation with $10$ generators and $25$ relators and prove that both numbers are minimal among all finite presentations. For $n=3$, we show that $π_1(X\\setminus W)$ admits a presentation with $4$ generators and $78$ relators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31421",
  "author_total": 2,
  "authors": [
    {
      "name": "Shomrik Bhattacharya"
    },
    {
      "name": "Yuki Matsubara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4xmfabmre2gqb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31421",
  "fulltext_url": null,
  "id": "4xmfabmre2gqb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31421",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214627211",
  "pdf_url": "https://arxiv.org/pdf/2609.31421",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4xmfabmre2gqb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31421",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31421"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Fundamental groups of complements of wobbly divisors in intersections of two quadrics",
  "title_text": "Fundamental groups of complements of wobbly divisors in intersections of two quadrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/4xmfabmre2gqb",
  "venue": "arXiv",
  "versions": []
}