{
  "abstract": "A combination of recent results of Canning--Larson--Payne--Willwacher and Payne--Willwacher is that the motivic Euler characteristic of the moduli space $M_{g,n}$ of nonsingular curves with $n$ markings is polynomial in the Tate motive if and only if $g=0$ or $3g+2n<25$. In the cases when $g\\geq 1$ and $3g+2n<25$, there are $32$ pairs $(g,n)$ where the motivic Euler characteristic has been computed. We compute the motivic Euler characteristic for $9$ more pairs, leaving only $6$ pairs where the motivic Euler characteristic is polynomial but unknown. In genus $4$, we moreover compute the answer when $n=7$, i.e.~the first non-polynomial case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09694",
  "author_total": 4,
  "authors": [
    {
      "name": "Jonas Bergström"
    },
    {
      "name": "Samir Canning"
    },
    {
      "name": "Dan Petersen"
    },
    {
      "name": "Johannes Schmitt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6apwtzpx2yrz1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09694",
  "fulltext_url": null,
  "id": "6apwtzpx2yrz1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09694",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220962812",
  "pdf_url": "https://arxiv.org/pdf/2610.09694",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6apwtzpx2yrz1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09694",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09694"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Motivic Euler characteristics of moduli spaces of curves",
  "title_text": "Motivic Euler characteristics of moduli spaces of curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/6apwtzpx2yrz1",
  "venue": "arXiv",
  "versions": []
}