The aim of this book is to study 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, a concept
previously introduced by the author, this work isolates those varieties
where the fundamental group influences global properties of the
canonical class.
The book is primarily geared toward 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. The methods are drawn from diverse sources,
including Atiyah's L2 -index theorem, Gromov's theory of Poincaré
series, and recent generalizations of Kodaira's vanishing theorem.
Originally published in 1995.
The Princeton Legacy Library uses the latest print-on-demand
technology to again make available previously out-of-print books from
the distinguished backlist of Princeton University Press. These editions
preserve the original texts of these important books while presenting
them in durable paperback and hardcover editions. The goal of the
Princeton Legacy Library is to vastly increase access to the rich
scholarly heritage found in the thousands of books published by
Princeton University Press since its founding in 1905.
