Okounkov Bodies of Complexity-One T-Varieties

2011/08/02 by Lars Petersen, Petersen, Lars
Mathematics · #14C20 #14L30 #14M25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14C20 #msc:14L30 #msc:14M25

paper · pdf · doi:10.48550/arxiv.1108.0632

25 pages, 12 figures

arxiv created 2011/08/02 · openalex publication_date 2011/08/02 · arxiv updated 2011/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute Okounkov bodies of projective complexity-one T-varieties with respect to two types of invariant flags. In particular, we show that the latter are rational polytopes. Moreover, using results of Dave Anderson and Nathan Ilten, we briefly exhibit explicit links to degenerations and T-deformations. Finally, we prove that the global Okounkov body of a rational projective complexity-one T-variety is rational polyhedral.

Citations

• Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory
• Canonical divisors on T-varieties

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