Nevanlinna theory in several variables

Summary

Nevanlinna theory in several variables is the value distribution theory of holomorphic maps whose source or target has dimension greater than one. Its model case is a holomorphic curve $f \colon \C \to \mathbb{P}^n$, studied against hyperplanes, and more generally holomorphic maps from $\C^m$ to projective varieties, studied against divisors. It extends the one-variable Nevanlinna theory, with a characteristic function, counting functions and proximity functions, and first and second main theorems. It is closely tied to Kobayashi hyperbolicity and, through an analogy found by Vojta, to Diophantine approximation.