{
  "id": "2408.06616",
  "version": "v1",
  "published": "2024-08-13T04:06:13.000Z",
  "updated": "2024-08-13T04:06:13.000Z",
  "title": "Gromov-Witten invariants in family and quantum cohomology",
  "authors": [
    "Indranil Biswas",
    "Nilkantha Das",
    "Jeongseok Oh",
    "Anantadulal Paul"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "A moduli space of stable maps to the fibers of a fiber bundle is constructed. The new moduli space is a family version of the classical moduli space of stable maps to a non-singular complex projective variety. The virtual cycle for this moduli space is also constructed, and an analogue of Gromov-Witten invariants is defined. As an application, we recover the formula for the number of rational degree d curves in P3, whose image lies in a plane in P3 (known as planar curves in P3), intersecting r general lines while passing through given s general points, where r + 2s = 3d + 2, firstly proved by R. Mukherjee, R. Kumar Singh and the fourth named author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-13T04:06:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N35"
    ],
    "keywords": [
      "gromov-witten invariants",
      "quantum cohomology",
      "stable maps",
      "non-singular complex projective variety",
      "classical moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}