Riemann Surfaces by Way of Complex Analytic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Riemann Surfaces by Way of Complex Analytic Geometry write by Dror Varolin. This book was released on 2011-08-10. Riemann Surfaces by Way of Complex Analytic Geometry available in PDF, EPUB and Kindle. 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. This book is the first to give a textbook exposition of Riemann surface theory from the viewpoint of positive Hermitian line bundles and Hormander $\bar \partial$ 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introduction to the methods used currently in complex geometry, as exemplified in J. P. Demailly's online but otherwise unpublished book ``Complex analytic and differential geometry.''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. --Steven Zelditch
Algebraic Curves and Riemann Surfaces
Algebraic Curves and Riemann Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Curves and Riemann Surfaces write by Rick Miranda. This book was released on 1995. Algebraic Curves and Riemann Surfaces available in PDF, EPUB and Kindle. In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.
A Course in Complex Analysis and Riemann Surfaces
A Course in Complex Analysis and Riemann Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course in Complex Analysis and Riemann Surfaces write by Wilhelm Schlag. This book was released on 2014-08-06. A Course in Complex Analysis and Riemann Surfaces available in PDF, EPUB and Kindle. Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.
Lectures on Vector Bundles over Riemann Surfaces. (MN-6), Volume 6
Lectures on Vector Bundles over Riemann Surfaces. (MN-6), Volume 6 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Vector Bundles over Riemann Surfaces. (MN-6), Volume 6 write by Robert C. Gunning. This book was released on 2020-09-01. Lectures on Vector Bundles over Riemann Surfaces. (MN-6), Volume 6 available in PDF, EPUB and Kindle. The description for this book, Lectures on Vector Bundles over Riemann Surfaces. (MN-6), Volume 6, will be forthcoming.
The Concept of a Riemann Surface
The Concept of a Riemann Surface - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Concept of a Riemann Surface write by Hermann Weyl. This book was released on 2013-12-31. The Concept of a Riemann Surface available in PDF, EPUB and Kindle. This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.
