Okounkov bodies and transfinite diameter

2017/01/03 by Sione Ma`u, Ma`u, Sione
Mathematics · #32U20 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.CV #msc:32U20

paper · pdf · doi:10.48550/arxiv.1701.00570

31 pages and 3 figures

arxiv created 2017/01/03 · openalex publication_date 2017/01/03 · arxiv updated 2017/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an explicit calculation of an Okounkov body associated to an algebraic variety. This is used to derive a formula for transfinite diameter on the variety. We relate this formula to a recent result of D. Witt Nystrom.

Related

• Volumes of Arithmetic Okounkov Bodies
• Relations between Transfinite Diameters on Affine Algebraic Varieties
• Geometric aspects of Newton-Okounkov bodies
• Chebyshev constants, transfinite diameter, and computation on complex\n algebraic curves
• Functions on Okounkov bodies coming from geometric valuations (with an appendix by Sébastien Boucksom)