{
  "annotation_id": "07d279a4-943e-4407-a091-51c2d06c103d",
  "date_created": "2026-02-17T05:53:16.282000Z",
  "date_modified": "2026-02-17T05:53:16.282000Z",
  "file_hash": "6ea983693c172167552253971bbb1da64cc5bf1e6b2952343311926bf4bd5a82",
  "private": false,
  "record": {
    "abstract": "In this paper we compute an explicit closed formula for the total Tjurina number $\\tau(C)$ of a reduced projective plane curve $C$ in terms of the graded Betti numbers of the corresponding Jacobian algebra. This formula allows a completely new view point on the classical upper bounds for the total Tjurina number $\\tau(C)$ of a plane curve $C$ given by A. du Plessis and C. T. C. Wall. This approach yields in particular a new necessary condition for a set of positive integers to be the graded Betti numbers of the Jacobian algebra of a reduced plane curve.",
    "arxiv_id": "2601.08583",
    "authors": [
      "Alexandru Dimca",
      "Gabriel Sticlaru"
    ],
    "categories": [
      "math.AG",
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Graded Betti numbers of the Jacobian algebra and total Tjurina numbers of plane curves",
    "url": "https://arxiv.org/abs/2601.08583",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "591c5094-3669-46ef-9eca-eb7e68c74c13",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}