2020/03/22 by Luo, Wenbin
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2003.09837
In the setting of Arakelov geometry over adelic curves, we introduce the χ-volume function and show some general properties. This article is dedicated to talk about the continuity of χ-volume function. By discussing its relationship with volume function, we prove its continuity around adelic ℚ-ample ℚ-Cartier divisors and its continuity in the trivially valued case. The study of the variation of arithmetic Okounkov bodies leads us to its continuous extension on arithmetic surfaces.