Continuous extension of arithmetic volumes

2008/09/06 by Atsushi Moriwaki, Moriwaki, Atsushi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.0809.1129

33 pages

arxiv created 2008/09/06 · openalex publication_date 2008/09/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is the sequel of the paper "Continuity of volumes on arithmetic varieties", in which we established the arithmetic volume function of smooth hermitian Q-invertible sheaves and proved its continuity. The continuity of the volume function has a lot of applications as treated in the paper as above. In this paper, we would like to consider its continuous extension over R.

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