{
  "id": "1409.2026",
  "version": "v1",
  "published": "2014-09-06T16:01:32.000Z",
  "updated": "2014-09-06T16:01:32.000Z",
  "title": "Okounkov bodies for ample line bundles with applications to multiplicities for group representations",
  "authors": [
    "Henrik Seppänen"
  ],
  "comment": "supersedes the preprint arXiv:1007.1915",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "Let $\\mathscr{L} \\rightarrow X$ be an ample line bundle over a complex normal projective variety $X$. We construct a flag $X_0 \\subseteq X_1 \\subseteq \\cdots \\subseteq X_n=X$ of subvarieties for which the associated Okounkov body for $\\mathscr{L}$ is a rational polytope. In the case when $X$ is a homogeneous surface, and the pseudoeffective cone of $X$ is rational polyhedral, we also show that the global Okounkov body is a rational polyhedral cone if the flag of subvarieties is suitably chosen. Finally, we provide an application to the asymptotic study of group representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-06T16:01:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ample line bundle",
      "group representations",
      "application",
      "multiplicities",
      "global okounkov body"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.2026S"
    }
  }
}