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511.33 --- Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- 511.33 Analytical and multiplicative number theory. Asymptotics. Sieves etc.

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Number theory --- Number Theory --- #WBIB:dd.Lic.L.De Busschere --- Number study --- Numbers, Theory of --- Algebra --- 511.33 --- 511.33 Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- Analytical and multiplicative number theory. Asymptotics. Sieves etc.

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Number theory --- Cribles (Mathématiques) --- Sieves (Mathematics) --- #WWIS:ALTO --- 511.33 --- Number sieves --- Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- Sieves (Mathematics). --- 511.33 Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- Cribles (Mathématiques) --- Analytical and multiplicative number theory. Asymptotics. Sieves etc --- Theorie des nombres --- Cribles (mathematiques) --- Theorie multiplicative

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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 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.

Shafarevich maps --- Complex manifolds --- Automorphic forms --- 511.33 --- Mappings (Mathematics) --- Analytic spaces --- Manifolds (Mathematics) --- Automorphic functions --- Forms (Mathematics) --- Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- 511.33 Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- Analytical and multiplicative number theory. Asymptotics. Sieves etc --- Automorphic forms. --- Shafarevich maps. --- Complex manifolds.

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Aims Theaimofthisbookistoprovideaguidetoarichandfascinatings- ject: algebraic curves, and how they vary in families. The revolution that the ?eld of algebraic geometry has undergone with the introd- tion of schemes, together with new ideas, techniques and viewpoints introduced by Mumford and others, have made it possible for us to understandthebehaviorofcurvesinwaysthatsimplywerenotpos- ble a half-century ago. This in turn has led, over the last few decades, to a burst of activity in the area, resolving long-standing problems and generating new and unforeseen results and questions. We hope to acquaint you both with these results and with the ideas that have made them possible. The book isn’t intended to be a de?nitive reference: the subject is developing too rapidly for that to be a feasible goal, even if we had the expertise necessary for the task. Our preference has been to - cus on examples and applications rather than on foundations. When discussing techniques we’ve chosen to sacri?ce proofs of some, even basic,results—particularlywherewecanprovideagoodreference— inordertoshowhowthemethodsareusedtostudymoduliofcurves. Likewise, we often prove results in special cases which we feel bring out the important ideas with a minimum of technical complication.

512.77 --- 511.33 --- Algebraic curves. Algebraic surfaces. Three-dimensional algebraic varieties --- Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- Curves, Algebraic. --- Moduli theory. --- 511.33 Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- 512.77 Algebraic curves. Algebraic surfaces. Three-dimensional algebraic varieties --- Moduli theory --- Mathematics. --- Algebraic geometry. --- Algebraic Geometry. --- Curves, Algebraic --- Theory of moduli --- Analytic spaces --- Functions of several complex variables --- Geometry, Algebraic --- Algebraic curves --- Algebraic varieties --- Analytical and multiplicative number theory. Asymptotics. Sieves etc --- Geometry, algebraic. --- Algebraic geometry --- Geometry