We show that the height of a variety over a finitely generated field of characteristic zero can be written as an integral of local heights over the set of places of the field. This allows us to apply our previous work on toric varieties and extend our combinatorial formulae for the height to compute some arithmetic intersection numbers of nontoric arithmetic varieties over the rational numbers.
"Height of varieties over finitely generated fields." Kyoto J. Math. 56 (1) 13 - 32, April 2016. https://doi.org/10.1215/21562261-3445138