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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Riemann Surfaces by Way of Complex Analytic Geometry (Hardcover, New ed.)
Loot Price: R2,745
Discovery Miles 27 450
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Riemann Surfaces by Way of Complex Analytic Geometry (Hardcover, New ed.)
Series: Graduate Studies in Mathematics
Expected to ship within 12 - 17 working days
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This book establishes the basic function theory and complex
geometry of Riemann surfaces, both open and compact. Many of the
methods used in the book are adaptations and simplifications of
methods from the theories of several complex variables and complex
analytic geometry and would serve as excellent training for
mathematicians wanting to work in complex analytic geometry. After
three introductory chapters, the book embarks on its central, and
certainly most novel, goal of studying Hermitian holomorphic line
bundles and their sections. Among other things,
finite-dimensionality of spaces of sections of holomorphic line
bundles of compact Riemann surfaces and the triviality of
holomorphic line bundles over Riemann surfaces are proved, with
various applications. Perhaps the main result of the book is
Hoermander's Theorem on the square-integrable solution of the
Cauchy-Riemann equations. The crowning application is the proof of
the Kodaira and Narasimhan Embedding Theorems for compact and open
Riemann surfaces. The intended reader has had first courses in real
and complex analysis, as well as advanced calculus and basic
differential topology (though the latter subject is not crucial).
As such, the book should appeal to a broad portion of the
mathematical and scientific community.
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