Several Complex Variables And Complex Geometry

Author : Joseph L. Taylor
Publisher : American Mathematical Soc.
Page : 530 pages
File Size : 50,7 Mb
Release : 2002
Category : Functions of several complex variables
ISBN : 9780821831786

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Several Complex Variables with Connections to Algebraic Geometry and Lie Groups by Joseph L. Taylor Pdf

This text presents an integrated development of core material from several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraicsheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest arethe last three chapters, which are devoted to applications of the preceding material to the study of the structure theory and representation theory of complex semisimple Lie groups. Included are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Milicic's proof of the Borel-Weil-Bott theorem,which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for theexpert.

Author : John P. D'Angelo
Publisher : Routledge
Page : 319 pages
File Size : 40,5 Mb
Release : 2019-07-16
Category : Mathematics
ISBN : 9781351416719

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Several Complex Variables and the Geometry of Real Hypersurfaces by John P. D'Angelo Pdf

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.

Author : Eric Bedford
Publisher : American Mathematical Soc.
Page : 368 pages
File Size : 49,9 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821814918

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Several Complex Variables and Complex Geometry, Part III by Eric Bedford Pdf

Author : S. Coen
Publisher : Routledge
Page : 500 pages
File Size : 47,5 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351445276

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Geometry and Complex Variables by S. Coen Pdf

This reference presents the proceedings of an international meeting on the occasion of theUniversity of Bologna's ninth centennial-highlighting the latest developments in the field ofgeometry and complex variables and new results in the areas of algebraic geometry,differential geometry, and analytic functions of one or several complex variables.Building upon the rich tradition of the University of Bologna's great mathematics teachers, thisvolume contains new studies on the history of mathematics, including the algebraic geometrywork of F. Enriques, B. Levi, and B. Segre ... complex function theory ideas of L. Fantappie,B. Levi, S. Pincherle, and G. Vitali ... series theory and logarithm theory contributions of P.Mengoli and S. Pincherle ... and much more. Additionally, the book lists all the University ofBologna's mathematics professors-from 1860 to 1940-with precise indications of eachcourse year by year.Including survey papers on combinatorics, complex analysis, and complex algebraic geometryinspired by Bologna's mathematicians and current advances, Geometry and ComplexVariables illustrates the classic works and ideas in the field and their influence on today'sresearch.

Author : Robert C. Gunning,Hugo Rossi
Publisher : American Mathematical Society
Page : 334 pages
File Size : 52,8 Mb
Release : 2022-08-25
Category : Mathematics
ISBN : 9781470470661

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Analytic Functions of Several Complex Variables by Robert C. Gunning,Hugo Rossi Pdf

The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. After initial successes by Poincaré and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable. Beginning in the 1930s, initially through the work of Oka, then H. Cartan, and continuing with the work of Grauert, Remmert, and others, new tools were introduced into the theory of several complex variables that resolved many of the open problems and fundamentally changed the landscape of the subject. These tools included a central role for sheaf theory and increased uses of topology and algebra. The book by Gunning and Rossi was the first of the modern era of the theory of several complex variables, which is distinguished by the use of these methods. The intention of Gunning and Rossi's book is to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces. Fundamental concepts and techniques are discussed as early as possible. The first chapter covers material suitable for a one-semester graduate course, presenting many of the central problems and techniques, often in special cases. The later chapters give more detailed expositions of sheaf theory for analytic functions and the theory of complex analytic spaces. Since its original publication, this book has become a classic resource for the modern approach to functions of several complex variables and the theory of analytic spaces. Further information about this book, including updates, can be found at the following URL: www.ams.org/publications/authors/books/postpub/chel-368.

Author : Wolfgang Ebeling
Publisher : American Mathematical Soc.
Page : 334 pages
File Size : 49,6 Mb
Release : 2007
Category : Functions of several complex variables
ISBN : 9780821833193

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Functions of Several Complex Variables and Their Singularities by Wolfgang Ebeling Pdf

The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.

Author : Jiri Lebl
Publisher : Lulu.com
Page : 142 pages
File Size : 48,6 Mb
Release : 2016-05-05
Category : Electronic
ISBN : 9781365095573

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Tasty Bits of Several Complex Variables by Jiri Lebl Pdf

This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.

Author : Peter Ebenfelt,Norbert Hungerbühler,Joseph J. Kohn,Ngaiming Mok,Emil J. Straube
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 52,8 Mb
Release : 2011-01-30
Category : Mathematics
ISBN : 9783034600095

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Complex Analysis by Peter Ebenfelt,Norbert Hungerbühler,Joseph J. Kohn,Ngaiming Mok,Emil J. Straube Pdf

This volume presents the proceedings of a conference on Several Complex Variables, PDE’s, Geometry, and their interactions held in 2008 at the University of Fribourg, Switzerland, in honor of Linda Rothschild.

Author : H. Grauert,Thomas Peternell,R. Remmert
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 52,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662098738

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Several Complex Variables VII by H. Grauert,Thomas Peternell,R. Remmert Pdf

The first survey of its kind, written by internationally known, outstanding experts who developed substantial parts of the field. The book contains an introduction written by Remmert, describing the history of the subject, and is very useful to graduate students and researchers in complex analysis, algebraic geometry and differential geometry.

Author : R. Michael Range
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 50,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475719185

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Holomorphic Functions and Integral Representations in Several Complex Variables by R. Michael Range Pdf

The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.

Author : Klaus Fritzsche,Hans Grauert
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468492736

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From Holomorphic Functions to Complex Manifolds by Klaus Fritzsche,Hans Grauert Pdf

This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.

Author : Michael Schneider,Yum-Tong Siu
Publisher : Cambridge University Press
Page : 582 pages
File Size : 43,5 Mb
Release : 1999
Category : Mathematics
ISBN : 0521770866

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Several Complex Variables by Michael Schneider,Yum-Tong Siu Pdf

Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.

Author : Vincenzo Ancona,Edoardo Ballico,Rosa M Miro-Roig,Alessandro Silva
Publisher : CRC Press
Page : 204 pages
File Size : 45,8 Mb
Release : 1997-04-27
Category : Mathematics
ISBN : 058229276X

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Complex Analysis and Geometry by Vincenzo Ancona,Edoardo Ballico,Rosa M Miro-Roig,Alessandro Silva Pdf

Based on two conferences held in Trento, Italy, this volume contains 13 research papers and two survey papers on complex analysis and complex algebraic geometry. The main topics addressed by these leading researchers include: Mori theory polynomial hull vector bundles q-convexity Lie groups and actions on complex spaces hypercomplex structures pseudoconvex domains projective varieties Peer-reviewed and extensively referenced, Complex Analysis and Geometry contains recent advances and important research results. It also details several problems that remain open, the resolution of which could further advance the field.

Author : Vasiliy Sergeyevich Vladimirov,Scripta Technica
Publisher : Courier Corporation
Page : 370 pages
File Size : 53,6 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 9780486458120

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Methods of the Theory of Functions of Many Complex Variables by Vasiliy Sergeyevich Vladimirov,Scripta Technica Pdf

This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. The text begins with an introduction that defines the basic concepts and elementary propositions, along with the more salient facts from the theory of functions of real variables and the theory of generalized functions. Subsequent chapters address the theory of plurisubharmonic functions and pseudoconvex domains, along with characteristics of domains of holomorphy. These explorations are further examined in terms of four types of domains: multiple-circular, tubular, semitubular, and Hartogs' domains. Surveys of integral representations focus on the Martinelli-Bochner, Bergman-Weil, and Bochner representations. The final chapter is devoted to applications, particularly those involved in field theory. It employs the theory of generalized functions, along with the theory of functions of several complex variables.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,9 Mb
Release : 1991
Category : Electronic
ISBN : OCLC:872459097

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1991 Mathematics Subject Classification by Anonim Pdf