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Differentiability of the arithmetic volume function along the base conditions
Hideaki Ikoma
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…
On subfiniteness of graded linear series
Huayi Chen, Hideaki Ikoma
Hilbert's 14th problem studies the finite generation property of the intersection of an integral algebra of finite type with a subfield of the field of fractions of the algebra. It…
Adelic Cartier divisors with base conditions and the continuity of volumes
Hideaki Ikoma
In the previous paper [7], we introduced a notion of pairs of adelic R-Cartier divisors and R-base conditions. The purpose of this paper is to propose an extended notion of adelic…
Adelic Cartier divisors with base conditions and the Bonnesen-Diskant-type inequalities
Hideaki Ikoma
In this paper, we introduce positivity notions for pairs of adelic R-Cartier divisors and R-base conditions, and study fundamental properties of the arithmetic volumes defined for…
Remarks on the arithmetic restricted volumes and the arithmetic base loci
Hideaki Ikoma
In this paper, we collect some fundamental properties of the arithmetic restricted volumes (or the arithmetic multiplicities) of the adelically metrized line bundles. The arithmeti…
A numerical characterization of nef adelic divisors
Hideaki Ikoma
To a generically big adelic divisor, we can associate an arithmetic Okounkov body, which is a pair of the geometric Okounkov body and the concave transform of the Green functions.…