{
  "id": "2302.02085",
  "version": "v1",
  "published": "2023-02-04T04:07:06.000Z",
  "updated": "2023-02-04T04:07:06.000Z",
  "title": "Semicontinuous maps on module varieties",
  "authors": [
    "Christof Geiß",
    "Daniel Labardini-Fragoso",
    "Jan Schröer"
  ],
  "comment": "17 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that $g$-vectors and $E$-invariants of modules are upper semicontinuous. We also discuss inequalities of generic values of some upper semicontinuous maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-04T04:07:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "module varieties",
      "study semicontinuous maps",
      "finite-dimensional algebras",
      "upper semicontinuous maps",
      "truncated euler maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}