Complex Analytic Geometry: From The Localization Viewpoint PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Complex Analytic Geometry: From The Localization Viewpoint PDF full book. Access full book title Complex Analytic Geometry: From The Localization Viewpoint by Tatsuo Suwa. Download full books in PDF and EPUB format.
Author: Tatsuo Suwa Publisher: World Scientific ISBN: 9814704296 Category : Mathematics Languages : en Pages : 609
Book Description
Complex Analytic Geometry is a subject that could be termed, in short, as the study of the sets of common zeros of complex analytic functions. It has a long history and is closely related to many other fields of Mathematics and Sciences, where numerous applications have been found, including a recent one in the Sato hyperfunction theory.This book is concerned with, among others, local invariants that arise naturally in Complex Analytic Geometry and their relations with global invariants of the manifold or variety. The idea is to look at them as residues associated with the localization of some characteristic classes. Two approaches are taken for this — topological and differential geometric — and the combination of the two brings out further fruitful results. For this, on one hand, we present detailed description of the Alexander duality in combinatorial topology. On the other hand, we give a thorough presentation of the Čech-de Rham cohomology and integration theory on it. This viewpoint provides us with the way for clearer and more precise presentations of the central concepts as well as fundamental and important results that have been treated only globally so far. It also brings new perspectives into the subject and leads to further results and applications.The book starts off with basic material and continues by introducing characteristic classes via both the obstruction theory and the Chern-Weil theory, explaining the idea of localization of characteristic classes and presenting the aforementioned invariants and relations in a unified way from this perspective. Various related topics are also discussed. The expositions are carried out in a self-containing manner and includes recent developments. The profound consequences of this subject will make the book useful for students and researchers in fields as diverse as Algebraic Geometry, Complex Analytic Geometry, Differential Geometry, Topology, Singularity Theory, Complex Dynamical Systems, Algebraic Analysis and Mathematical Physics.
Author: Tatsuo Suwa Publisher: World Scientific ISBN: 9814704296 Category : Mathematics Languages : en Pages : 609
Book Description
Complex Analytic Geometry is a subject that could be termed, in short, as the study of the sets of common zeros of complex analytic functions. It has a long history and is closely related to many other fields of Mathematics and Sciences, where numerous applications have been found, including a recent one in the Sato hyperfunction theory.This book is concerned with, among others, local invariants that arise naturally in Complex Analytic Geometry and their relations with global invariants of the manifold or variety. The idea is to look at them as residues associated with the localization of some characteristic classes. Two approaches are taken for this — topological and differential geometric — and the combination of the two brings out further fruitful results. For this, on one hand, we present detailed description of the Alexander duality in combinatorial topology. On the other hand, we give a thorough presentation of the Čech-de Rham cohomology and integration theory on it. This viewpoint provides us with the way for clearer and more precise presentations of the central concepts as well as fundamental and important results that have been treated only globally so far. It also brings new perspectives into the subject and leads to further results and applications.The book starts off with basic material and continues by introducing characteristic classes via both the obstruction theory and the Chern-Weil theory, explaining the idea of localization of characteristic classes and presenting the aforementioned invariants and relations in a unified way from this perspective. Various related topics are also discussed. The expositions are carried out in a self-containing manner and includes recent developments. The profound consequences of this subject will make the book useful for students and researchers in fields as diverse as Algebraic Geometry, Complex Analytic Geometry, Differential Geometry, Topology, Singularity Theory, Complex Dynamical Systems, Algebraic Analysis and Mathematical Physics.
Author: Antonio Alarcón Publisher: Springer Nature ISBN: 3030690563 Category : Mathematics Languages : en Pages : 430
Book Description
This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.
Author: Mark Green Publisher: American Mathematical Soc. ISBN: 1470410125 Category : Mathematics Languages : en Pages : 314
Book Description
This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.
Author: Vincenzo Ancona Publisher: CRC Press ISBN: 9780582292765 Category : Mathematics Languages : en Pages : 204
Book Description
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: Carles Broto Publisher: Birkhäuser ISBN: 3034890184 Category : Mathematics Languages : en Pages : 405
Book Description
Central to this collection of papers are new developments in the general theory of localization of spaces. This field has undergone tremendous change of late and is yielding new insight into the mysteries of classical homotopy theory. The present volume comprises the refereed articles submitted at the Conference on Algebraic Topology held in Sant Feliu de Guíxols, Spain, in June 1994. Several comprehensive articles on general localization clarify the basic tools and give a report on the state of the art in the subject matter. The text is therefore accessible not only to the professional mathematician but also to the advanced student.
Author: Jörg Eschmeier Publisher: Oxford University Press ISBN: 9780198536673 Category : Language Arts & Disciplines Languages : en Pages : 378
Book Description
Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, various concepts from function theory and complex analytic geometry are drawn together to give a new approach to concrete spectral computations and give insights into new developments in the spectral theory of linear operators. Classical results from cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the language of homological algebra. The advantages of this approach are illustrated by a variety of examples, unexpected applications, and conceptually new ideas that should stimulate further research among mathematicians.
Author: José Luis Cisneros-Molina Publisher: Springer Nature ISBN: 3030957608 Category : Mathematics Languages : en Pages : 822
Book Description
This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Author: Juan Tirao Publisher: Springer Science & Business Media ISBN: 1461241626 Category : Mathematics Languages : en Pages : 330
Book Description
The representation theory of Lie groups plays a central role in both clas sical and recent developments in many parts of mathematics and physics. In August, 1995, the Fifth Workshop on Representation Theory of Lie Groups and its Applications took place at the Universidad Nacional de Cordoba in Argentina. Organized by Joseph Wolf, Nolan Wallach, Roberto Miatello, Juan Tirao, and Jorge Vargas, the workshop offered expository courses on current research, and individual lectures on more specialized topics. The present vol ume reflects the dual character of the workshop. Many of the articles will be accessible to graduate students and others entering the field. Here is a rough outline of the mathematical content. (The editors beg the indulgence of the readers for any lapses in this preface in the high standards of historical and mathematical accuracy that were imposed on the authors of the articles. ) Connections between flag varieties and representation theory for real re ductive groups have been studied for almost fifty years, from the work of Gelfand and Naimark on principal series representations to that of Beilinson and Bernstein on localization. The article of Wolf provides a detailed introduc tion to the analytic side of these developments. He describes the construction of standard tempered representations in terms of square-integrable partially harmonic forms (on certain real group orbits on a flag variety), and outlines the ingredients in the Plancherel formula. Finally, he describes recent work on the complex geometry of real group orbits on partial flag varieties.
Author: Siegfried Bosch Publisher: Springer ISBN: 3319044176 Category : Mathematics Languages : en Pages : 255
Book Description
The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
Author: David Eisenbud Publisher: Springer Science & Business Media ISBN: 1461253500 Category : Mathematics Languages : en Pages : 784
Book Description
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Author: Tatsuo Suwa
Author: Tatsuo Suwa
Author: Antonio Alarcón
Author: Mark Green
Author: Vincenzo Ancona
Author: Carles Broto
Author: Jörg Eschmeier
Author: José Luis Cisneros-Molina
Author: Juan Tirao
Author: Siegfried Bosch
Author: David Eisenbud