{
  "abstract": "The flat DHS connection $\\mathcal J_{\\mathrm{DHS}}$ constructed in arXiv:2602.01461 is smooth on the configuration space of $n$ points on a fixed compact Riemann surface $Σ$ of arbitrary genus $h$, takes values in an infinite-dimensional Lie algebra $\\hat{\\mathfrak t}_{h,n}$ and is invariant under the modular group $\\mathrm{Sp}(2h,\\mathbb Z)$. This paper is the first in a series for a program whose goal is to extend the connection $\\mathcal J_{\\mathrm{DHS}}$ to a global flat connection on the Teichmüller space $\\mathcal T_{h,n}$ valued in the Lie algebra of derivations of $\\hat{\\mathfrak t}_{h,n}$. Upon the choice of local coordinates adapted to the map $\\mathcal T_{h,n}\\to \\mathcal T_h$, such a connection splits into three pieces: $\\mathcal J_{\\mathrm{DHS}}$, a piece $\\mathcal L$ corresponding to holomorphic directions of $\\mathcal T_h$ and a third piece corresponding to anti-holomorphic directions in $\\mathcal T_h$. In this paper, we isolate the system of equations satisfied by $\\mathcal L$ and obtain its solution locally and explicitly. The construction of a global extension of $\\mathcal J_{\\mathrm{DHS}}$ to $\\mathcal T_{h,n}$ and the extension of the meromorphic connection of arXiv:1112.0864 to $\\mathcal T_{h,n}$, are relegated to future publications in this series.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29169",
  "author_total": 4,
  "authors": [
    {
      "name": "Eric D'Hoker"
    },
    {
      "name": "Benjamin Enriquez"
    },
    {
      "name": "Oliver Schlotterer"
    },
    {
      "name": "Federico Zerbini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0hjh68453z84d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29169",
  "fulltext_url": null,
  "id": "0hjh68453z84d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29169",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204938548",
  "pdf_url": "https://arxiv.org/pdf/2608.29169",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0hjh68453z84d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2608.29169",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29169"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Flat connections on moduli spaces I: Local (1,0)-extension of the DHS connection",
  "title_text": "Flat connections on moduli spaces I: Local (1,0)-extension of the DHS connection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/0hjh68453z84d",
  "venue": "arXiv",
  "versions": []
}