{
  "id": "1904.02453",
  "version": "v1",
  "published": "2019-04-04T10:15:54.000Z",
  "updated": "2019-04-04T10:15:54.000Z",
  "title": "Hodge ideals and spectrum of isolated hypersurface singularities",
  "authors": [
    "Seung-Jo Jung",
    "In-Kyun Kim",
    "Youngho Yoon",
    "Morihiko Saito"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We introduce Hodge ideal spectrum for isolated hypersurface singularities to see the difference between the Hodge ideals and the microlocal $V$-filtration modulo the Jacobian ideal. We compare the Hodge ideal spectrum with the Steenbrink spectrum that can be described by using the microlocal $V$-filtration. As a consequence of a formula of Mustata and Popa, these two spectra coincide in the weighted homogeneous case. We prove sufficient conditions for their coincidence and non-coincidence in some non-weighted-homogeneous cases where the defining function is semi-weighted-homogeneous or with non-degenerate Newton boundary in most cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-04T10:15:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isolated hypersurface singularities",
      "hodge ideal spectrum",
      "non-degenerate newton boundary",
      "jacobian ideal",
      "steenbrink spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}