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Differentiability of the $\chi$-volume function over an adelic curve

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arxiv 2303.03377 v2 pith:OMUWUKVC submitted 2023-03-06 math.AG math.NT

Antoine Sédillot This is my paper · ORCID
classification math.AGmath.NT
keywords adelicresultcurvedifferentiabilityfunctionvolumeampleapplication
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abstract

In this article, we show a differentiability property for the $\chi$-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.

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  1. Concave transforms of compactified S-metrized divisors

    math.AG 2025-05 conditional novelty 7.0 of 10

    For big compactified S-metrized divisors on quasi-projective varieties over adelic curves, concave transforms are constructed and shown to satisfy arithmetic volume and Hilbert-Samuel formulas.

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