{
  "annotation_id": "f04da9b8-7af4-43c6-96b3-8402655893dc",
  "date_created": "2026-02-17T05:53:16.295000Z",
  "date_modified": "2026-02-17T05:53:16.295000Z",
  "file_hash": "c8c7630dbbdcd49e358643968ef42e60143ad0042cfc767afccfa89410e0aa92",
  "private": false,
  "record": {
    "abstract": "We study $\\mathbb{S}_n$-equivariant motivic invariants of the moduli space $\\mathcal{M}_{g, n}(\\mathbb{P}^r, d)$ of degree-$d$ maps from $n$-pointed curves of genus $g$ to $\\mathbb{P}^r$. In particular, we obtain formulas for the Serre characteristic, which specializes to the Hodge--Deligne polynomial. Fixing $g, r \\geq 1$, we prove that an explicit invertible transform of the generating function for the Serre characteristics is rational. We use our formula to prove a stability result for the weight-graded compactly-supported Euler characteristics of $\\mathcal{M}_{g, n}(\\mathbb{P}^r, d)$ as $d \\to \\infty$. In genus one and two, we reduce the calculation of the Serre characteristic of $\\mathcal{M}_{g, n}(\\mathbb{P}^r, d)$ to those of the moduli spaces $\\mathcal{M}_{g, n}$ of $n$-pointed curves. Since Getzler has calculated the Serre characteristic of $\\mathcal{M}_{1, n}$, our formula in particular determines the Serre characteristic of $\\mathcal{M}_{1, n}(\\mathbb{P}^r, d)$ for arbitrary $n$, $r$, and $d$. Our formula also calculates the Serre characteristic of $\\mathcal{M}_{2, n}(\\mathbb{P}^r, d)$ whenever those of $\\mathcal{M}_{2, n +k}$ are known for $k \\leq d$.",
    "arxiv_id": "2601.07981",
    "authors": [
      "Siddarth Kannan",
      "Terry Dekun Song"
    ],
    "categories": [
      "math.AG",
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "title": "Virtual Hodge numbers of $\\mathcal{M}_{g, n}(\\mathbb{P}^r, d)$: stability and calculations",
    "url": "https://arxiv.org/abs/2601.07981",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cdfd9158-4ed1-4e68-8b4d-0e7cd0586f04",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}