{
  "id": "0906.1264",
  "version": "v2",
  "published": "2009-06-06T10:52:47.000Z",
  "updated": "2010-09-02T09:07:27.000Z",
  "title": "Twisted genera of symmetric products",
  "authors": [
    "Laurentiu Maxim",
    "Joerg Schuermann"
  ],
  "comment": "The paper has been rewritten (and shortend), emphasizing more the view point of pre-lambda rings, with the main abstract assumptions weakend. In this corrected form it applies now also to mixed Hodge modules by our recent joint paper with M. Saito (arXiv:1008.5345), which contains all technical details about symmetric products of mixed Hodge modules as used here",
  "journal": "Selecta Math. (N.S.) 18 (2012), no. 1, 283-317",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "We prove very general formulae for the generating series of (Hodge) genera of symmetric products with coefficients, which hold for complex quasi-projective varieties with any kind of singularities, and which include many of the classical results in the literature as special cases. Important specializations of our results include generating series for extensions of Hodge numbers and Hirzebruch genus to the singular setting and, in particular, generating series for Intersection cohomology Hodge numbers and Goresky-MacPherson Intersection cohomology signatures of symmetric products of complex projective varieties. A very general proof is given based on Kuenneth formulae and pre-lambda structures on the coefficient theory of a point. Moreover, Atiyah's approach to power operations in K-theory also works in this context, giving a nice description of the important related Adams operations. This last approach also allows us to introduce very interesting coefficients on the symmetric products.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-02T09:07:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55S15",
      "20C30",
      "32S35",
      "32S60",
      "19L20"
    ],
    "keywords": [
      "symmetric products",
      "twisted genera",
      "generating series",
      "intersection cohomology hodge numbers",
      "goresky-macpherson intersection cohomology signatures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.1264M"
    }
  }
}