{
  "annotation_id": "44668b7c-b69f-4a9e-8e95-0a1c8f0bb6e1",
  "date_created": "2026-02-17T05:53:08.702000Z",
  "date_modified": "2026-02-17T05:53:08.702000Z",
  "file_hash": "db8a109541c9317c1434d691f55981d4eac97426d3d468127f2b184884a1c582",
  "private": false,
  "record": {
    "abstract": "In this paper we study the connection between Herzog ideals (i.e., ideals with a squarefree Gr\\\"obner degeneration) and $F$-singularities. More precisely, we show that, in positive characteristic, homogeneous Herzog ideals define $F$-anti-nilpotent rings, and we inquire, in characteristic 0, on a surprising relationship between being Herzog ideals after a change of coordinates and defining rings of dense open $F$-pure type.",
    "arxiv_id": "2601.06476",
    "authors": [
      "Alessandro De Stefani",
      "Linquan Ma",
      "Matteo Varbaro"
    ],
    "categories": [
      "math.AC",
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Herzog ideals and $F$-singularities",
    "url": "https://arxiv.org/abs/2601.06476",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3eee2341-a8f2-467c-bfdb-de14bb278af4",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}