Shafarevich Maps and Automorphic Forms

This text studies various geometric properties and algebraic invariants of smooth projective varieties with infinite fundamental groups. This approach allows for much interplay between methods of algebraic geometry, complex analysis, the theory of harmonic maps and topology. Making systematic use of Shafarevich maps, this work isolates those varieties where the fundamental group influences global properties of the canonical class. The book is primarily geared towards researchers and graduate students in algebraic geometry who are interested in the structure and classification theory of algebraic varieties. There are, however, presentations of many other applications involving other topics as well – such as Abelian varieties, theta functions and automorphic forms on bounded domains.