Related papers: Continuous extension of arithmetic volumes
We introduce the volume function for hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence,…
In the setting of Arakelov geometry over adelic curves, we introduce the $\chi$-volume function and show some general properties. This article is dedicated to talk about the continuity of $\chi$-volume function. By discussing its…
We introduce the positive intersection product in Arakelov geometry and prove that the arithmetic volume function is continuously differentiable. As applications, we compute the distribution function of the asymptotic measure of a Hermitian…
By some result on the study of arithemtic over trivially valued field, we find its applications to Arakelov geometry over adelic curves. We prove a partial result of the continuity of arithmetic $\chi$-volume along semiample divisors.…
The aim of this paper is twofold. First we prove a theorem of extension of sections of a coherent subquotient of a hermitian vector bundle on a complex analytic space with control of the norms, without any of the smoothness assumptions that…
We introduce an adelic Cartier divisor over a trivially valued field and discuss the bigness of it. For bigness, we give the integral representation of the arithmetic volume and prove the existence of limit of it. Moreover, we show that the…
We introduce a new arithmetic invariant for hermitian line bundles on an arithmetic variety. We use this invariant to measure the variation of the volume function with respect to the metric. The main result of this paper is a generalized…
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 R-Cartier divisors that we call an l1-adelic R-Cartier…
For a hermitian line bundle over an arithmetic variety, we construct a convex continuous function on the Okounkov body associated to the generic fibre of the line bundle. The integration of the continuous function gives the growth of the…
The volume of a Cartier divisor is an asymptotic invariant, which measures the rate of growth of sections of powers of the divisor. It extends to a continuous, homogeneous, and log-concave function on the whole N\'eron--Severi space, thus…
It is proved that the volume of spherical or hyperbolic simplices, when considered as a function of the dihedral angles, can be extended continuously to degenerated simplices.
We consider a space of infinitely smooth functions on an unbounded closed convex set in ${\mathbb R}^n$. It is shown that each function of this space can be extended to an entire function in ${\mathbb C}^n$ satisfying some prescribed growth…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
In his paper "On the Schlafli differential equality", J. Milnor conjectured that the volume of n-dimensional hyperbolic and spherical simplices, as a function of the dihedral angles, extends continuously to the closure of the space of…
The main result of this paper is a proof of the continuity of a family of integral functionals defined on the space of functions of bounded variation with respect to a topology under which smooth functions are dense. These functionals occur…
We establish, for a generically big Hermitian line bundle, the convergence of truncated Harder-Narasimhan polygons and the uniform continuity of the limit. As applications, we prove a conjecture of Moriwaki asserting that the arithmetic…
We develop a continued fraction algorithm in finite extensions of $\Q_p$ generalising certain algorithms in $\Q_p$, and prove the finiteness property for certain small degree extensions. We also discuss the metrical properties of the…
We study the behavior of volumes of divisors in a family. We show that the volume of a divisor on the generic fiber equals the infimum of its volumes on fibers over any dense subset of the base. As an application, we show that the volume…
We study the continuity regularity of functions in the complex Sobolev spaces. As applications, we obtain Hermitian generalizations of a recent result due Guedj-Guenancia-Zeriahi on the diameters of Kaehler metrics.
We introduce a notion of complexity of a complex of ell-adic sheaves on a quasi-projective variety and prove that the six operations are "continuous", in the sense that the complexity of the output sheaves is bounded solely in terms of the…