Hi!

I have a fairly good background in Algebraic Geometry (say at the level of Hartshorne's book and some Intersection Theory from Fulton) and since I think working over $\text{Spec } \mathbb{Z}$ is fun, I would like to learn some Arakelov Theory.

My background in differential geometry and analysis is not that good, though - I know basic definitions in both fields and have taken some courses, but I have forgot a lot, and what more, I seem to need complex differential geometry, which I have never studied. From what I understand, residuce currents is important in Arakelov Theory.

So my question is:

**What books, what articles should I read to get a good analytical / complex differential geometric background (covering for example, residue currents) sufficient to study Arakelov Theory?**