On the concavity of the arithmetic volumes

2013/10/31 by Hideaki Ikoma, Ikoma, Hideaki
Mathematics · #Algebraic Geometry (math.AG) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1310.8424

openalex publication_date 2013/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we study the differentiability of the arithmetic volumes along arithmetic R-divisors, and give some equality conditions for the Brunn-Minkowski inequality for arithmetic volumes over the cone of nef and big arithmetic R-divisors.

Related

• Differentiability of the arithmetic volume function along the base conditions
• Adelic divisors on arithmetic varieties
• Adelic Cartier divisors with base conditions and the Bonnesen-Diskant-type inequalities
• Volumes of Arithmetic Okounkov Bodies
• Volume function over a trivially valued field