{
  "id": "2310.02844",
  "version": "v1",
  "published": "2023-10-04T14:21:44.000Z",
  "updated": "2023-10-04T14:21:44.000Z",
  "title": "The heart fan of an abelian category",
  "authors": [
    "Nathan Broomhead",
    "David Pauksztello",
    "David Ploog",
    "Jon Woolf"
  ],
  "comment": "30 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "We apply convex geometry (cones, fans) to homological input (abelian categories,hearts of bounded t-structures) to construct a new invariant of an abelian category, its heart fan. When the abelian category is the module category of a finite-dimensional algebra, the heart fan is complete and contains the g-fan as the subfan of full-dimensional simplicial cones. The heart fan is also closely related to the wall-and-chamber structure for King semistability, and to the Hall algebra scattering diagram.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-04T14:21:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G80",
      "16E35",
      "14F08",
      "18E40",
      "52A20"
    ],
    "keywords": [
      "abelian category",
      "heart fan",
      "hall algebra scattering diagram",
      "full-dimensional simplicial cones",
      "wall-and-chamber structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}