Diophantine Geometry: An Introduction
《Diophantine Geometry: An Introduction》 · 第 174 页 · Section B.2「Heights on Projective Space」，Definition
For $P=(x_0,\ldots,x_n)\in\mathbb P^n(k)$, the logarithmic height is $h_k(P)=\log H_k(P)=\sum_{v\in M_k}-n_v\min\{v(x_0),\ldots,v(x_n)\}$.