Differentiability of the arithmetic volume function along the base conditions

2018/07/31 by Hideaki Ikoma, Ikoma, Hideaki
Mathematics · #37P30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Primary 14G40 #Secondary 11G50

paper · pdf · doi:10.48550/arxiv.1807.11680

openalex publication_date 2018/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that the arithmetic volume function defined on the space of pairs of adelic R-Cartier divisors and base conditions is differentiable at a big pair, and that its derivative is given by an arithmetic restricted positive intersection number defined for the pair.

Related

• Adelic Cartier divisors with base conditions and the Bonnesen-Diskant-type inequalities
• Volume function over a trivially valued field
• On the concavity of the arithmetic volumes
• Differentiability of Adelic Volumes and Equidistribution on Quasi-Projective Varieties
• Adelic divisors on arithmetic varieties