Several Complex Variables And Complex Geometry Part I PDF Download
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Author | : Joseph L. Taylor |
Publisher | : American Mathematical Soc. |
Total Pages | : 530 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 082183178X |
Download Several Complex Variables with Connections to Algebraic Geometry and Lie Groups Book in PDF, ePub and Kindle
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 | : Eric Bedford |
Publisher | : American Mathematical Soc. |
Total Pages | : 280 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : 0821814893 |
Download Several Complex Variables and Complex Geometry, Part I Book in PDF, ePub and Kindle
Author | : Robert Clifford Gunning |
Publisher | : American Mathematical Soc. |
Total Pages | : 338 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821821652 |
Download Analytic Functions of Several Complex Variables Book in PDF, ePub and Kindle
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.
Author | : John P. D'Angelo |
Publisher | : Routledge |
Total Pages | : 287 |
Release | : 2019-07-16 |
Genre | : Mathematics |
ISBN | : 1351416723 |
Download Several Complex Variables and the Geometry of Real Hypersurfaces Book in PDF, ePub and Kindle
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 | : E. Bedford Steven George Krantz D'Angelo |
Publisher | : American Mathematical Soc. |
Total Pages | : 292 |
Release | : |
Genre | : |
ISBN | : 9780821868188 |
Download Several complex variables and complex geometry, Part I Book in PDF, ePub and Kindle
Author | : Wolfgang Ebeling |
Publisher | : American Mathematical Soc. |
Total Pages | : 334 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821833197 |
Download Functions of Several Complex Variables and Their Singularities Book in PDF, ePub and Kindle
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 | : Peter Ebenfelt |
Publisher | : Springer Science & Business Media |
Total Pages | : 353 |
Release | : 2011-01-30 |
Genre | : Mathematics |
ISBN | : 3034600097 |
Download Complex Analysis Book in PDF, ePub and Kindle
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 | : S. Coen |
Publisher | : CRC Press |
Total Pages | : 522 |
Release | : 1991-06-03 |
Genre | : Mathematics |
ISBN | : 9780824784454 |
Download Geometry and Complex Variables Book in PDF, ePub and Kindle
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'sresearc
Author | : Fangyang Zheng |
Publisher | : American Mathematical Soc. |
Total Pages | : 275 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821829602 |
Download Complex Differential Geometry Book in PDF, ePub and Kindle
Discusses the differential geometric aspects of complex manifolds. This work contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. It discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles. It also gives a brief account of the surface classification theory.
Author | : Gen Komatsu |
Publisher | : Springer Science & Business Media |
Total Pages | : 322 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461221668 |
Download Analysis and Geometry in Several Complex Variables Book in PDF, ePub and Kindle
This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Since the inhomogeneous Cauchy-Riemann equation was introduced in the study of Complex Analysis of Several Variables, there has been strong interaction between Complex Analysis and Real Analysis, in particular, the theory of Partial Differential Equations. Problems in Complex Anal ysis stimulate the development of the PDE theory which subsequently can be applied to Complex Analysis. This interaction involves Differen tial Geometry, for instance, via the CR structure modeled on the induced structure on the boundary of a complex manifold. Such structures are naturally related to the PDE theory. Differential Geometric formalisms are efficiently used in settling problems in Complex Analysis and the results enrich the theory of Differential Geometry. This volume focuses on the most recent developments in this inter action, including links with other fields such as Algebraic Geometry and Theoretical Physics. Written by participants in the Symposium, this vol ume treats various aspects of CR geometry and the Bergman kernel/ pro jection, together with other major subjects in modern Complex Analysis. We hope that this volume will serve as a resource for all who are interested in the new trends in this area. We would like to express our gratitude to the Taniguchi Foundation for generous financial support and hospitality. We would also like to thank Professor Kiyosi Ito who coordinated the organization of the symposium.