Complex Analytic Sets
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Complex Analytic Sets
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Author : E.M. Chirka
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Complex Analytic Sets written by E.M. Chirka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The theory of complex analytic sets is part of the modern geometrical theory of functions of several complex variables. A wide circle of problems in multidimensional complex analysis, related to holomorphic functions and maps, can be reformulated in terms of analytic sets. In these reformulations additional phenomena may emerge, while for the proofs new methods are necessary. (As an example we can mention the boundary properties of conformal maps of domains in the plane, which may be studied by means of the boundary properties of the graphs of such maps.) The theory of complex analytic sets is a relatively young branch of complex analysis. Basically, it was developed to fulfill the need of the theory of functions of several complex variables, but for a long time its development was, so to speak, within the framework of algebraic geometry - by analogy with algebraic sets. And although at present the basic methods of the theory of analytic sets are related with analysis and geometry, the foundations of the theory are expounded in the purely algebraic language of ideals in commutative algebras. In the present book I have tried to eliminate this noncorrespondence and to give a geometric exposition of the foundations of the theory of complex analytic sets, using only classical complex analysis and a minimum of algebra (well-known properties of polynomials of one variable). Moreover, it must of course be taken into consideration that algebraic geometry is one of the most important domains of application of the theory of analytic sets, and hence a lot of attention is given in the present book to algebraic sets.
Lectures On Stratification Of Complex Analytic Sets
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Author : Marie-Hélène Schwartz
language : en
Publisher:
Release Date : 1966
Lectures On Stratification Of Complex Analytic Sets written by Marie-Hélène Schwartz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Topology categories.
Introduction To Complex Analytic Geometry
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Author : Stanislaw Lojasiewicz
language : en
Publisher: Birkhäuser
Release Date : 2013-03-09
Introduction To Complex Analytic Geometry written by Stanislaw Lojasiewicz and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
facts. An elementary acquaintance with topology, algebra, and analysis (in cluding the notion of a manifold) is sufficient as far as the understanding of this book is concerned. All the necessary properties and theorems have been gathered in the preliminary chapters -either with proofs or with references to standard and elementary textbooks. The first chapter of the book is devoted to a study of the rings Oa of holomorphic functions. The notions of analytic sets and germs are introduced in the second chapter. Its aim is to present elementary properties of these objects, also in connection with ideals of the rings Oa. The case of principal germs (§5) and one-dimensional germs (Puiseux theorem, §6) are treated separately. The main step towards understanding of the local structure of analytic sets is Ruckert's descriptive lemma proved in Chapter III. Among its conse quences is the important Hilbert Nullstellensatz (§4). In the fourth chapter, a study of local structure (normal triples, § 1) is followed by an exposition of the basic properties of analytic sets. The latter includes theorems on the set of singular points, irreducibility, and decom position into irreducible branches (§2). The role played by the ring 0 A of an analytic germ is shown (§4). Then, the Remmert-Stein theorem on re movable singularities is proved (§6). The last part of the chapter deals with analytically constructible sets (§7).
Complex Analytic Sets
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Author : Evgeniĭ Mikhaĭlovich Chirka
language : en
Publisher:
Release Date : 1985
Complex Analytic Sets written by Evgeniĭ Mikhaĭlovich Chirka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Science
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Author : Andrew John Sommese
language : en
Publisher: World Scientific
Release Date : 2005
The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Science written by Andrew John Sommese and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Written by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980's to the most recent research on positive dimensional sets.
Geometry Of Subanalytic And Semialgebraic Sets
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Author : Masahiro Shiota
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometry Of Subanalytic And Semialgebraic Sets written by Masahiro Shiota and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Real analytic sets in Euclidean space (Le. , sets defined locally at each point of Euclidean space by the vanishing of an analytic function) were first investigated in the 1950's by H. Cartan [Car], H. Whitney [WI-3], F. Bruhat [W-B] and others. Their approach was to derive information about real analytic sets from properties of their complexifications. After some basic geometrical and topological facts were established, however, the study of real analytic sets stagnated. This contrasted the rapid develop ment of complex analytic geometry which followed the groundbreaking work of the early 1950's. Certain pathologies in the real case contributed to this failure to progress. For example, the closure of -or the connected components of-a constructible set (Le. , a locally finite union of differ ences of real analytic sets) need not be constructible (e. g. , R - {O} and 3 2 2 { (x, y, z) E R : x = zy2, x + y2 -=I- O}, respectively). Responding to this in the 1960's, R. Thorn [Thl], S. Lojasiewicz [LI,2] and others undertook the study of a larger class of sets, the semianalytic sets, which are the sets defined locally at each point of Euclidean space by a finite number of ana lytic function equalities and inequalities. They established that semianalytic sets admit Whitney stratifications and triangulations, and using these tools they clarified the local topological structure of these sets. For example, they showed that the closure and the connected components of a semianalytic set are semianalytic.
Introduction To Complex Analysis
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Author : E.M. Chirka
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Complex Analysis written by E.M. Chirka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the reviews: "... In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. Some of the individual articles are reminiscent in style of the early volumes of the first Ergebnisse series and will probably prove to be equally useful as a reference; ...for the appropriate reader, they will be valuable sources of information about modern complex analysis." Bulletin of the Am.Math.Society, 1991 "... This remarkable book has a helpfully informal style, abundant motivation, outlined proofs followed by precise references, and an extensive bibliography; it will be an invaluable reference and a companion to modern courses on several complex variables." ZAMP, Zeitschrift für Angewandte Mathematik und Physik, 1990
Introduction To Complex Analysis
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Author : Boris Vladimirovich Shabat
language : en
Publisher: American Mathematical Soc.
Release Date : 1992-11-04
Introduction To Complex Analysis written by Boris Vladimirovich Shabat and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-04 with Mathematics categories.
Since the 1960s, there has been a flowering in higher-dimensional complex analysis. Both classical and new results in this area have found numerous applications in analysis, differential and algebraic geometry, and, in particular, contemporary mathematical physics. In many areas of modern mathematics, the mastery of the foundations of higher-dimensional complex analysis has become necessary for any specialist. Intended as a first study of higher-dimensional complex analysis, this book covers the theory of holomorphic functions of several complex variables, holomorphic mappings, and submanifolds of complex Euclidean space.
Analytic D Modules And Applications
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Author : Jan-Erik Björk
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Analytic D Modules And Applications written by Jan-Erik Björk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This is the first monograph to be published on analytic D-modules and it offers a complete and systematic treatment of the foundations together with a thorough discussion of such modern topics as the Riemann--Hilbert correspondence, Bernstein--Sata polynomials and a large variety of results concerning microdifferential analysis. Analytic D-module theory studies holomorphic differential systems on complex manifolds. It brings new insight and methods into many areas, such as infinite dimensional representations of Lie groups, asymptotic expansions of hypergeometric functions, intersection cohomology on Kahler manifolds and the calculus of residues in several complex variables. The book contains seven chapters and has an extensive appendix which is devoted to the most important tools which are used in D-module theory. This includes an account of sheaf theory in the context of derived categories, a detailed study of filtered non-commutative rings and homological algebra, and the basic material in symplectic geometry and stratifications on complex analytic sets. For graduate students and researchers.
An Introduction To Complex Analysis And Geometry
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Author : John P. D'Angelo
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
An Introduction To Complex Analysis And Geometry written by John P. D'Angelo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Functions of complex variables categories.
Provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The first four chapters provide an introduction to complex analysis with many elementary and unusual applications. Chapters 5 to 7 develop the Cauchy theory and include some striking applications to calculus. Chapter 8 glimpses several appealing topics, simultaneously unifying the book and opening the door to further study.