{
  "id": "1101.0352",
  "version": "v2",
  "published": "2011-01-01T16:52:45.000Z",
  "updated": "2011-07-03T19:54:10.000Z",
  "title": "Equivariant Chow cohomology of nonsimplicial toric varieties",
  "authors": [
    "Hal Schenck"
  ],
  "comment": "11 pages 3 figures v2 references added, typos fixed",
  "journal": "Transactions of the A.M.S., 364 (2012) 4041-4051",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a toric variety X_P determined by a rational polyhedral fan P in a lattice N, Payne shows that the equivariant Chow cohomology of X_P is the Sym(N)--algebra C^0(P) of integral piecewise polynomial functions on P. We use the Cartan-Eilenberg spectral sequence to analyze the associated reflexive sheaf on Proj(N), showing that the Chern classes depend on subtle geometry of P and giving criteria for the splitting of the sheaf as a sum of line bundles. For certain fans associated to the reflection arrangement A_n, we describe a connection between C^0(P) and logarithmic vector fields tangent to A_n.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-03T19:54:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "14F23",
      "13D40",
      "52C99"
    ],
    "keywords": [
      "toric variety",
      "equivariant chow cohomology",
      "nonsimplicial toric varieties",
      "logarithmic vector fields tangent",
      "integral piecewise polynomial functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.0352S"
    }
  }
}