Algebroid Mappings and Their Equidistribution Theory

Abstract

In this paper, the concept of algebroid mappings of complex manifolds is introduced based on that a large number of complex systems of PDEs admit multi-valued solutions that can be defined by a system of independent algebraic equations over the field of meromorphic functions. It is well-known that Nevanlinna theory is an important tool in complex ODE theory. To develop a similar tool applied to the study of algebroid solutions of complex systems of PDEs, one explores the equidistribution theory of algebroid mappings. Via uniformizating an algebroid mapping, we obtain a second main theorem of algebroid mappings from a complete K\"ahler manifold into a complex projective manifold provided that some certain conditions are imposed.