Okounkov bodies for ample line bundles with applications to multiplicities for group representations

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• 作者：Henrik Seppänen
• 关键词：Ample line bundle ; Okounkov body ; Irreducible representation ; Branching laws
• 刊名：Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：57
• 期：4
• 页码：735-749
• 全文大小：472 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra
  Convex and Discrete Geometry
  Geometry
  Algebraic Geometry
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2191-0383
• 卷排序：57

文摘

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 simplex. 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 for a generic choice of a flag of subvarieties. Finally, we provide an application to the asymptotic study of group representations.