Riemann Surfaces by Way of Complex Analytic Geometry (Graduate Studies in Mathematics)

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9780821853696: Riemann Surfaces by Way of Complex Analytic Geometry (Graduate Studies in Mathematics)

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 Hörmander'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. This book is the first to give a textbook exposition of Riemann surface theory from the viewpoint of positive Hermitian line bundles and Hörmander $\bar \partial$ estimates. It is more analytical and PDE oriented than prior texts in the field, and is an excellent introduction to the methods used currently in complex geometry, as exemplified in J. P. Demailly's online but otherwise unpublished book "Complex analytic and differential geometry." I used it for a one quarter course on Riemann surfaces and found it to be clearly written and self-contained. It not only fills a significant gap in the large textbook literature on Riemann surfaces but is also rather indispensible for those who would like to teach the subject from a differential geometric and PDE viewpoint.

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About the Author:

Dror Varolin is at Stony Brook University, NY, USA.

Review:

...the text will be very helpful for those who want to study Riemann surfaces from a differential geometric and PDE viewpoint. --Montash Math

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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97808218536960000000

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Descripción American Mathematical Society, United States, 2011. Hardback. Estado de conservación: New. New ed.. Language: English . Brand New Book. 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 Hormander 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. Nº de ref. de la librería AAN9780821853696

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Descripción American Mathematical Society, 2011. HRD. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería CE-9780821853696

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Descripción American Mathematical Society, United States, 2011. Hardback. Estado de conservación: New. New ed.. Language: English . Brand New Book. 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 Hormander 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. Nº de ref. de la librería AAN9780821853696

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Descripción American Mathematical Society, 2011. Hardcover. Estado de conservación: New. Nº de ref. de la librería DADAX0821853694

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Descripción American Mathematical Society. Hardback. Estado de conservación: new. BRAND NEW, Riemann Surfaces by Way of Complex Analytic Geometry, Dror Varolin, 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 Hormander'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. Nº de ref. de la librería B9780821853696

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Descripción American Mathematical Society, 2011. Estado de conservación: New. Establishes the basic function theory and complex geometry of Riemann surfaces, both open and compact. Series: Graduate Studies in Mathematics. Num Pages: 252 pages. BIC Classification: PBKD; PBMS. Category: (G) General (US: Trade). Dimension: 262 x 183 x 18. Weight in Grams: 614. . 2011. Hardcover. . . . . . Nº de ref. de la librería V9780821853696

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Descripción American Mathematical Society, 2011. Estado de conservación: New. book. Nº de ref. de la librería ria9780821853696_rkm

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Descripción American Mathematical Society. Estado de conservación: New. Establishes the basic function theory and complex geometry of Riemann surfaces, both open and compact. Series: Graduate Studies in Mathematics. Num Pages: 252 pages. BIC Classification: PBKD; PBMS. Category: (G) General (US: Trade). Dimension: 262 x 183 x 18. Weight in Grams: 614. . 2011. Hardcover. . . . . Books ship from the US and Ireland. Nº de ref. de la librería V9780821853696

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