{
  "id": "2108.00875",
  "version": "v1",
  "published": "2021-08-02T13:19:03.000Z",
  "updated": "2021-08-02T13:19:03.000Z",
  "title": "Intersecting $ψ$-classes on $M_{0,w}^{\\mathrm{trop}}$",
  "authors": [
    "Marvin Anas Hahn",
    "Shiyue Li"
  ],
  "comment": "25 pages; comments welcome",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "In this paper, we study the intersection products of weighted tropical $\\psi$-classes, in arbitrary dimensions, on the moduli space of tropical weighted stable curves. We introduce the tropical Gromov--Witten multiplicity at each vertex of a given tropical curve. This concept enables us to prove that the weight of a maximal cone in an intersection of $\\psi$-classes decomposes as the product of tropical Gromov--Witten multiplicities at all vertices of the cone's associated tropical curves. Along the way, we define weighted tropical $\\psi$-classes on these moduli spaces, furnish a combinatorial characterisation thereof and realise them as multiples of tropical Weil divisors of a family of rational functions on these moduli spaces. In the special case of top-dimensional intersections, our result confirms the correspondence between the tropical Gromov--Witten invariants and their algebro-geometric counterparts explicitly on these weighted moduli spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-02T13:19:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E14",
      "05E14",
      "05E14",
      "14N35",
      "14T15"
    ],
    "keywords": [
      "moduli space",
      "tropical gromov-witten multiplicity",
      "tropical curve",
      "combinatorial characterisation thereof",
      "intersecting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}