Complex Analytic Cycles Ii
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Complex Analytic Cycles Ii
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Author : Daniel Barlet
language : en
Publisher: Springer
Release Date : 2025-06-25
Complex Analytic Cycles Ii written by Daniel Barlet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-25 with Mathematics categories.
This book is the second volume of a work on complex analytic cycles and the results, stated without proof in the first volume, are proved here. It begins with the construction of the reduced complex space formed by all compact cycles of a given complex space. Following this construction the main subjects of the book are: • Fundamental class of a cycle and relative fundamental class of an analytic family of cycles • Intersection theory with parameters on complex manifolds and more generally on nearly smooth complex spaces • Holomorphic currents on reduced complex spaces • Chow varieties and cycle spaces of quasi-projective complex spaces • Natural morphism from the Douady space to the cycle space • Holomorphic convexity in cycle spaces and integration of $\bar{partial}$-cohomology classes on cycles • Strong Kählerianity of cycle spaces of Kähler manifolds • Numerous important applications of cycle space theory Preliminaries needed in the book in addition to the material of the first volume, for instance sheaf cohomology with support, are explained in detail, making this two-volume work quite self-contained. The French version of the present book was published in 2020 by the French Mathematical Society in the series Cours Spécialisés and during the translation process the authors have in many ways improved the original version.
Complex Analytic Cycles Ii
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Author : Daniel Barlet
language : en
Publisher: Springer Nature
Release Date : 2025-06-23
Complex Analytic Cycles Ii written by Daniel Barlet and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-23 with Mathematics categories.
This book is the second volume of a work on complex analytic cycles and the results, stated without proof in the first volume, are proved here. It begins with the construction of the reduced complex space formed by all compact cycles of a given complex space. Following this construction the main subjects of the book are: • Fundamental class of a cycle and relative fundamental class of an analytic family of cycles • Intersection theory with parameters on complex manifolds and more generally on nearly smooth complex spaces • Holomorphic currents on reduced complex spaces • Chow varieties and cycle spaces of quasi-projective complex spaces • Natural morphism from the Douady space to the cycle space • Holomorphic convexity in cycle spaces and integration of $\bar{partial}$-cohomology classes on cycles • Strong Kählerianity of cycle spaces of Kähler manifolds • Numerous important applications of cycle space theory Preliminaries needed in the book in addition to the material of the first volume, for instance sheaf cohomology with support, are explained in detail, making this two-volume work quite self-contained. The French version of the present book was published in 2020 by the French Mathematical Society in the series Cours Spécialisés and during the translation process the authors have in many ways improved the original version.
Complex Analytic Cycles I
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Author : Daniel Barlet
language : en
Publisher: Springer Nature
Release Date : 2020-01-03
Complex Analytic Cycles I written by Daniel Barlet and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-03 with Mathematics categories.
The book consists of a presentation from scratch of cycle space methodology in complex geometry. Applications in various contexts are given. A significant portion of the book is devoted to material which is important in the general area of complex analysis. In this regard, a geometric approach is used to obtain fundamental results such as the local parameterization theorem, Lelong' s Theorem and Remmert's direct image theorem. Methods involving cycle spaces have been used in complex geometry for some forty years. The purpose of the book is to systematically explain these methods in a way which is accessible to graduate students in mathematics as well as to research mathematicians. After the background material which is presented in the initial chapters, families of cycles are treated in the last most important part of the book. Their topological aspects are developed in a systematic way and some basic, important applications of analytic families of cycles are given. The construction of the cycle space as a complex space, along with numerous important applications, is given in the second volume. The present book is a translation of the French version that was published in 2014 by the French Mathematical Society.
Complex Analytic Cycles
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Author : Daniel Barlet
language : en
Publisher:
Release Date : 2019
Complex Analytic Cycles written by Daniel Barlet and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Geometry, Algebraic categories.
The book consists of a presentation from scratch of cycle space methodology in complex geometry. Applications in various contexts are given. A significant portion of the book is devoted to material which is important in the general area of complex analysis. In this regard, a geometric approach is used to obtain fundamental results such as the local parameterization theorem, Lelong' s Theorem and Remmert's direct image theorem. Methods involving cycle spaces have been used in complex geometry for some forty years. The purpose of the book is to systematically explain these methods in a way which is accessible to graduate students in mathematics as well as to research mathematicians. After the background material which is presented in the initial chapters, families of cycles are treated in the last most important part of the book. Their topological aspects are developed in a systematic way and some basic, important applications of analytic families of cycles are given. The construction of the cycle space as a complex space, along with numerous important applications, is given in the second volume. The present book is a translation of the French version that was published in 2014 by the French Mathematical Society.
Topological Transformations For Efficient Structural Analysis
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Author : Ali Kaveh
language : en
Publisher: Springer Nature
Release Date : 2022-10-23
Topological Transformations For Efficient Structural Analysis written by Ali Kaveh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-23 with Technology & Engineering categories.
The author has published many papers and books on topological transformations for optimal analysis of structures, where many methods and algorithms are developed. However, the framework of this book generalizes many concepts and makes the previously developed methods conceptually more attractive. The aim of the present work is two folds. On the one hand, it shows to mathematicians how the apparently pure mathematical concepts can be applied to the efficient solution of problems in structural mechanics. On the other hand, it illustrates to engineers the important role of mathematical concepts for the solution of engineering problems. The present framework provides efficient means for looking at problems and developing ideas by transforming the models (structures, networks, systems) to other spaces (higher dimension, lower dimension, or identical dimension) to simplify the problems. This book is attractive for those who look at the deeper aspects of concepts and helps the reader to develop his/her own ideas. In general, it opens a new horizon for improving the existing methods in civil, mechanical, and electrical engineering.
Several Complex Variables
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Author : Michael Schneider
language : en
Publisher: Cambridge University Press
Release Date : 1999
Several Complex Variables written by Michael Schneider and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.
Automorphic Forms And Related Geometry Assessing The Legacy Of I I Piatetski Shapiro
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Author : James W. Cogdell
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-01
Automorphic Forms And Related Geometry Assessing The Legacy Of I I Piatetski Shapiro written by James W. Cogdell 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 2014-04-01 with Mathematics categories.
This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.
Complex Analytic Geometry From The Localization Viewpoint
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Author : Tatsuo Suwa
language : en
Publisher: World Scientific
Release Date : 2024-02-21
Complex Analytic Geometry From The Localization Viewpoint written by Tatsuo Suwa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-21 with Mathematics categories.
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.
Multidimensional Residue Theory And Applications
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Author : Alekos Vidras
language : en
Publisher: American Mathematical Society
Release Date : 2023-10-18
Multidimensional Residue Theory And Applications written by Alekos Vidras and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-18 with Mathematics categories.
Residue theory is an active area of complex analysis with connections and applications to fields as diverse as partial differential and integral equations, computer algebra, arithmetic or diophantine geometry, and mathematical physics. Multidimensional Residue Theory and Applications defines and studies multidimensional residues via analytic continuation for holomorphic bundle-valued current maps. This point of view offers versatility and flexibility to the tools and constructions proposed, allowing these residues to be defined and studied outside the classical case of complete intersection. The book goes on to show how these residues are algebraic in nature, and how they relate and apply to a wide range of situations, most notably to membership problems, such as the Briançon–Skoda theorem and Hilbert's Nullstellensatz, to arithmetic intersection theory and to tropical geometry. This book will supersede the existing literature in this area, which dates back more than three decades. It will be appreciated by mathematicians and graduate students in multivariate complex analysis. But thanks to the gentle treatment of the one-dimensional case in Chapter 1 and the rich background material in the appendices, it may also be read by specialists in arithmetic, diophantine, or tropical geometry, as well as in mathematical physics or computer algebra.
The Collected Papers Of Wei Liang Chow
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Author : Shiing-shen Chern
language : en
Publisher: World Scientific
Release Date : 2002-09-23
The Collected Papers Of Wei Liang Chow written by Shiing-shen Chern and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-23 with Mathematics categories.
This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century. Prof Chow's name has become a household word in mathematics because of the Chow ring, Chow coordinates, and Chow's theorem on analytic sets in projective spaces. The Chow ring has many advantages and is widely used in intersection theory of algebraic geometry. Chow coordinates have been a very versatile tool in many aspects of algebraic geometry. Chow's theorem — that a compact analytic variety in a projective space is algebraic — is justly famous; it shows the close analogy between algebraic geometry and algebraic number theory.About Professor Wei-Liang ChowThe long and distinguished career of Prof Wei-Liang Chow (1911-95) as a mathematician began in China with professorships at the National Central University in Nanking (1936-37) and the National Tung-Chi University in Shanghai (1946-47), and ultimately led him to the United States, where he joined the mathematics faculty of Johns Hopkins University in Baltimore, Maryland, first as an associate professor from 1948 to 1950, then as a full professor from 1950 until his retirement in 1977.In addition to serving as chairman of the mathematics department at Johns Hopkins from 1955 to 1965, he was Editor-in-Chief of the American Journal of Mathematics from 1953 to 1977.