{
  "id": "1705.04248",
  "version": "v1",
  "published": "2017-05-11T15:39:28.000Z",
  "updated": "2017-05-11T15:39:28.000Z",
  "title": "Newton polyhedra, tropical geometry and the ring of condition for $(C^*)^n$",
  "authors": [
    "Boris Kazarnovskii",
    "Askold Khovanskii"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "The ring of conditions defined by C. De Conchini and C. Procesi is an intersection theory for algebraic cycles in a spherical homogeneous space. In the paper we consider the ring of conditions for the group $(C^*)^n$. Up to a big extend this ring can be reduced to the cohomology rings of smooth projective toric varieties. This ring also can be described using tropical geometry. We recall these known results and provide a new description of this ring in terms of convex integral polyhedra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-11T15:39:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "14T05",
      "14M17"
    ],
    "keywords": [
      "tropical geometry",
      "newton polyhedra",
      "convex integral polyhedra",
      "smooth projective toric varieties",
      "intersection theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}