Shafarevich Maps and Automorphic Forms

János Kollár (Autor)

Buch | Softcover

212 Seiten

2014
Princeton University Press (Verlag)
978-0-691-60790-0 (ISBN)

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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. Originally published in 1995.
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PrefaceAcknowledgmentsIntroduction3Ch. 1Lefschetz-Type Theorems for [pi][subscript 1]19Ch. 2Families of Algebraic Cycles27Ch. 3Shafarevich Maps and Variants36Ch. 4The Fundamental Group and the Classification of Algebraic Varieties49Ch. 5The Method of Poincare59Ch. 6The Method of Atiyah71Ch. 7Subjectivity of the Poincare Map81Ch. 8Ball Quotients92Ch. 9The Kodaira Vanishing Theorem105Ch. 10Generalizations of the Kodaira Vanishing Theorem115Ch. 11Vanishing of L[superscript 2]-Cohomologies127Ch. 12Rational Singularities and Hodge Theory133Ch. 13The Method of Gromov141Ch. 14Nonvanishing Theorems151Ch. 15Plurigenera in Etale Covers161Ch. 16Existence of Automorphic Forms167Ch. 17Applications to Abelian Varieties175Ch. 18Open Problems and Further Remarks183References191Index201

Erscheint lt. Verlag	14.7.2014
Reihe/Serie	Porter Lectures
Zusatzinfo	3 line drawings
Verlagsort	New Jersey
Sprache	englisch
Maße	152 x 229 mm
Gewicht	28 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-691-60790-7 / 0691607907
ISBN-13	978-0-691-60790-0 / 9780691607900
Zustand	Neuware