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, finitedimensionality 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 Hormander's Theorem on the squareintegrable solution of the CauchyRiemann equations. The crowning application is the proof of the Kodaira and Narasimhan Embedding Theorems for compact and open Riemann surfaces.< /p>
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.
About Dror Varolin
Dror Varolin is at Stony Brook University, NY, USA.
Details Book
Author  :  Dror Varolin 
Publisher  :  American Mathematical Society 
Data Published  :  15 September 2011 
ISBN  :  0821853694 
EAN  :  9780821853696 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  252 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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