Introduction to Complex Hyperbolic Spaces

Focusing on the interplay between hyperbolic spaces and diophantine geometry, the book presents a systematic exposition of recent results and conjectures in the field. It explores the relationship between hyperbolicity of projective varieties and the finiteness of rational points, while also addressing qualitative and quantitative conjectures, including those by Vojta and Noguchi. Divided into three main parts—complex analytic theory, differential geometry, and Nevanlinna theory—the chapters are designed to be logically independent, catering to a range of interests in the subject.