{
  "id": "1611.03017",
  "version": "v1",
  "published": "2016-11-09T17:16:09.000Z",
  "updated": "2016-11-09T17:16:09.000Z",
  "title": "Singularities of metrics on Hodge bundles and their topological invariants",
  "authors": [
    "Dennis Eriksson",
    "Gerard Freixas i Montplet",
    "Christophe Mourougane"
  ],
  "categories": [
    "math.AG",
    "math.CV",
    "math.DG"
  ],
  "abstract": "We consider degenerations of complex projective Calabi--Yau varieties and study the singularities of $L^2$, Quillen and BCOV metrics on Hodge and determinant bundles. The dominant and subdominant terms in the expansions of the metrics close to non-smooth fibers are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds. We also describe corresponding invariants for more general degenerating families in the case of the Quillen metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-09T17:16:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32",
      "58K55",
      "58J52",
      "58K65",
      "14J70"
    ],
    "keywords": [
      "hodge bundles",
      "singularities",
      "complex projective calabi-yau varieties",
      "limit hodge structures",
      "non-smooth fibers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}