{
  "abstract": "We compute the cellular $\\mathbb{A}^1$-homology of De Concini--Procesi wonderful models of subspace arrangements. For a building set $\\mathcal{G}$ over a field $k$, we identify the cellular $\\mathbb{A}^1$-chain complex of $\\mathbb{P}(\\mathcal{G})$ with an $η$-twisted nested-set complex carrying Milnor--Witt coefficients and derived orientation data. The key geometric input is a motivic blow-up calculation: for a blow-up along a smooth center of codimension $c$, the relevant connecting class is $(c-1)_εη$, hence it is zero for $c$ odd and $η$ for $c$ even. This replaces the parity condition in the computation of Rains by a Milnor--Witt attaching class. As a consequence, the part of cellular $\\mathbb{A}^1$-homology surviving after multiplication by $η$, and also the homology after inverting $η$, are expressed by the interval cohomology of the $2$-divisible subposet of the lattice generated by $\\mathcal{G}$. For the braid arrangement, the condition becomes the odd-block condition on partitions, yielding explicit decompositions for the cellular $\\mathbb{A}^1$-homology of $\\overline{\\mathcal M}_{0,N}$ and examples in low rank.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.29097",
  "author_total": 2,
  "authors": [
    {
      "name": "Haoyang Liu"
    },
    {
      "name": "Keyao Peng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ffvmgfb41x5rh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.29097",
  "fulltext_url": null,
  "id": "ffvmgfb41x5rh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.29097",
  "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"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7172306021",
  "pdf_url": "https://arxiv.org/pdf/2607.29097",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ffvmgfb41x5rh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2607.29097",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.29097"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Cellular $\\mathbb{A}^1$-homology of wonderful models of subspace arrangements",
  "title_text": "Cellular 𝔸^1-homology of wonderful models of subspace arrangements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/ffvmgfb41x5rh",
  "venue": "arXiv",
  "versions": []
}