Shafarevich Maps and Automorphic Forms
Janos Kollar, "Shafarevich Maps and Automorphic Forms"
Princeton University Press | 1995-07-24 | ISBN: 0691043817 | 176 pages | DjVu | 2,3 MB
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 Poincare series, and recent generalizations of Kodaira's vanishing theorem.
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Princeton University Press Shafarevich Maps And Automorphic Forms Harmonic Maps Algebraic Geometry Canonical Class Projective Varieties Index Theorem Classification Theory Fundamental Groups Abelian Varieties Algebraic Varieties Geometric Properties Kodai
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