{
  "id": "math/0305142",
  "version": "v2",
  "published": "2003-05-09T16:56:44.000Z",
  "updated": "2003-08-03T10:22:58.000Z",
  "title": "Chow rings of toric varieties defined by atomic lattices",
  "authors": [
    "Eva Maria Feichtner",
    "Sergey Yuzvinsky"
  ],
  "comment": "23 pages, 7 figures, final revision with minor changes, to appear in Invent. Math",
  "journal": "Invent. Math. 155 (2004) 515-536.",
  "doi": "10.1007/s00222-003-0327-2",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "We study a graded algebra D=D(L,G) defined by a finite lattice L and a subset G in L, a so-called building set. This algebra is a generalization of the cohomology algebras of hyperplane arrangement compactifications found in work of De Concini and Procesi. Our main result is a representation of D, for an arbitrary atomic lattice L, as the Chow ring of a smooth toric variety that we construct from L and G. We describe this variety both by its fan and geometrically by a series of blowups and orbit removal. Also we find a Groebner basis of the relation ideal of D and a monomial basis of D over Z.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-08-03T10:22:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "toric varieties",
      "chow ring",
      "smooth toric variety",
      "hyperplane arrangement compactifications",
      "arbitrary atomic lattice"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2004,
      "month": "Mar",
      "volume": 155,
      "number": 3,
      "pages": 515
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004InMat.155..515F"
    }
  }
}