Last edited by Sazahn
Sunday, July 26, 2020 | History

9 edition of Several complex variables and complex manifolds found in the catalog.

# Several complex variables and complex manifolds

## by Mike Field

Written in English

Subjects:
• Functions of several complex variables.,
• Complex manifolds.

• Edition Notes

Includes bibliographies and indexes.

Classifications The Physical Object Statement Mike Field. Series London Mathematical Society lecture note series ;, 65-66 LC Classifications QA331 .F56 1982 Pagination 2 v. ; Open Library OL3781503M ISBN 10 0521283019, 0521288886 LC Control Number 81021590

In mathematics, complex geometry is the study of complex manifolds, complex algebraic varieties, and functions of several complex variables. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis.   The main theme is the extension of geometric function theory methods and theorems to several complex variables. The papers present various results on the growth of mappings in various classes as well as observations about the boundary behavior of mappings, via developing and using some semi group methods.

Elementary theory of several complex variables In this chapter we study the n-dimensional complex vector space Cn and introduce some notation used throughout this book. After recalling geometric and topolog-ical notions such as connectedness or convexity we . This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz theorem, and Vanishing theorems. Some results and tools on deformation and uniformization of complex manifolds are also discussed. Topics in Several Complex Variables Topics in Several Complex Variables.

Function Theory In Several Complex Variables. Welcome,you are looking at books for reading, the Function Theory In Several Complex Variables, you will able to read or download in Pdf or ePub books and notice some of author may have lock the live reading for some of ore it need a FREE signup process to obtain the book.   Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the $$\bar\partial$$-Neumann problem, it has rapidly acquired a life of its own and has became an important topic .

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### Several complex variables and complex manifolds by Mike Field Download PDF EPUB FB2

$\begingroup$ Well,the objects of functions of several complex variables are manifolds with a complex topological vector space ore,they are the centerpieces of the bulk of postth century analysis and geometry and the tools of sheaf theory via commutative algebra are deeply interwoven in a result of all this,any "pure" approach-say,emphasizing.

Several Complex Variables and Complex Manifolds I (London Mathematical Society Lecture Note Series Book 65) - Kindle edition by Field, Mike.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Several Complex Variables and Complex Manifolds I (London Mathematical Society Lecture Note Series Book 5/5(1).

This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds was first published in It was intended be a synthesis of those topics and a broad introduction to the field.

The work as a whole will be useful to professional mathematicians or mathematical Cited by: Klaus Fritzsche and Hans Grauert, From Holomorphic Functions to Complex Manifolds,volume in the Graduate Texts in Mathematics series.

This book is an extensive revision of the authors’ book, Several Complex Variables, which is volume 38 in the Graduate Texts in Mathematics series.

The first two chapters are an introduction to. This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds was first published in It was intended be a synthesis of those topics and a broad introduction to the field.

The present book grew out of introductory lectures on the theory offunctions of several variables. Its intent is to make the reader familiar, by the discussion of examples and special cases, with the most important branches and methods of this theory, among them, e.g., the problems of holomorphic continuation, the algebraic treatment of power series, sheaf and cohomology.

The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions (, ,)on the space C n of n-tuples of complex numbers.

As in complex analysis, which is the case n = 1 but of a distinct character, these are not just any functions: they are supposed to be holomorphic or complex analytic, so that locally speaking they are power.

This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.

Thus problems in one complex variable lead, from the very beginning, to studies in several complex variables. Complex tori and moduli spaces are complex manifolds, i.e. Hausdorff spaces with local complex coordinates Z 1,Zn; holomorphic functions are, locally, those functions which are holomorphic in these coordinates.

th In the second. I have always had a soft spot for Gunning and Rossi ("Analytic Functions of Several Complex Variables"), probably because it is more "algebraic" in its approach) (sheaves, local rings, and so on.

Hormander's "Introduction to Complex Analysis in Several Variables" takes what I always thought was a more "analytic" approach. The lecture notes were prepared by Jonathan Campbell, a student in the class.

Inhomogeneous C.R. Equation, Riemann Equation in One Variable, Functions of Several Complex Variables: 3: The Inhomogeneous Cauchy-Riemann Equation in Several Variables, Hartog Theory of Complex Manifolds, Kaehler Manifolds: 7: Complex Manifolds: Affine and.

Purchase An Introduction to Complex Analysis in Several Variables, Volume 7 - 3rd Edition. Print Book & E-Book. ISBNBook Edition: 3. : Several Complex Variables VI: Complex Manifolds (Encyclopaedia of Mathematical Sciences) () by Barth, W. and a great selection of similar New, Used and Collectible Books available now at great Range: $95 -$ Several complex variables and complex manifolds II Mike Field This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those.

Basic treatment of the theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differential systems where data is analytic.

Also included is a theory of abstract complex manifolds of one complex dimension; holomorphic functions; Cauchy's integral, more. 2 Real and Complex Manifolds Some of the properties of holomorphic functions, like power series expansion, do extend from one variable to several variables.

They diﬀer, however, in many impor-tant aspects. It is therefore, not correct to consider the theory of several complexFile Size: 1MB.

Several Complex Variables By B. Malgrange Tata Institute of Fundamental Research Bombay 3 Complex analytic manifolds 19 4 Analytic Continuation 25 5 Envelopes of Holomorphy 29 equations to the case of functions of several variables).

Several Complex Variables 3. Welcome,you are looking at books for reading, the Several Complex Variables 3, you will able to read or download in Pdf or ePub books and notice some of author may have lock the live reading for some of ore it need a FREE signup process to obtain the book.

If it available for your country it will shown as book reader and. The book primarily aims at students starting to work in the field of complex analysis in several variables and teachers who want to prepare a university lecture.

Therefore, the book contains more than 50 examples and more than supporting exercises. Englisch. This book is a polished version of my course notes for MathSeveral Complex Variables, given in SpringSpringand Spring semesters at Oklahoma State University.

It should be suitable for a semester-long topics course or for self-study as an introduction to .several complex variables. The emphasis in arranging the program was on the more analytical aspects of that subject, with particular attention to the relations between complex analysis and partial differential equations, to the properties of pseudo-convexity and of Stein manifolds, and the relations between currents and analytic varieties.More editions of Several Complex Variables and Complex Manifolds II (London Mathematical Society Lecture Note Series) (Pt.2): Several Complex Variables and Complex Manifolds II (London Mathematical Society Lecture Note Series) (Pt.2): ISBN () Softcover, Cambridge University Press,