Differentiability of the $\chi$-volume function over an adelic curve
Algebraic Geometry
2023-11-06 v2 Number Theory
Abstract
In this article, we show a differentiability property for the -volume function on the ample cone of adelic line bundles over an adelic curve. This result is deduced from a non-Archimedean counterpart of a diffrentiability result of Witt Nystr\"om. As an application, we give a logarithmic equidistribution result over adelic curves.
Cite
@article{arxiv.2303.03377,
title = {Differentiability of the $\chi$-volume function over an adelic curve},
author = {Antoine Sédillot},
journal= {arXiv preprint arXiv:2303.03377},
year = {2023}
}
Comments
43 pages, comments are welcome! Second version, the differentiability property is extended to the non relative case (Theorem 1.2) and allows to give the logarithmic equidistribution result (Theorem 1.3)