PomeDefinition 10.6.3.A68F1B40919C A plurisubharmonic metric on $L$ is a quadratic metric of the form $h=h_0\mathrm e^{-\varphi }$ with $\varphi \in \mathrm{PSH}(X,c_1(L,h_0))$. It assigns the value zero to the zero vector, also over the pole set of $\varphi $, and the value $+\infty $ to a nonzero vector over a pole of $\varphi $. Its Chern current is
\[ c_1(L,h)=c_1(L,h_0)+\mathrm{dd}^{\mathrm{c}}\varphi . \]
Comments
Corrections, questions, and mathematical discussion are welcome. Sign in with GitHub to comment. Comments are public.