Complex Analytic Geometry From The Localization Viewpoint
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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.
Complex Analytic Geometry
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Author : Tatsuo Suwa
language : en
Publisher: World Scientific Publishing Company
Release Date : 2024-03-15
Complex Analytic Geometry written by Tatsuo Suwa and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-15 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.
Complex Analytic Geometry
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Author : Gerd Fischer
language : en
Publisher: Springer
Release Date : 2006-11-14
Complex Analytic Geometry written by Gerd Fischer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Minimal Surfaces From A Complex Analytic Viewpoint
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Author : Antonio Alarcón
language : en
Publisher: Springer Nature
Release Date : 2021-03-10
Minimal Surfaces From A Complex Analytic Viewpoint written by Antonio Alarcón and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.
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.
Introduction To Complex Analytic Geometry
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Author : Stanisław Łojasiewicz
language : en
Publisher: Birkhauser
Release Date : 1991
Introduction To Complex Analytic Geometry written by Stanisław Łojasiewicz and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Complex Analysis And Geometry
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Author : Vincenzo Ancona
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Complex Analysis And Geometry written by Vincenzo Ancona 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 2013-11-11 with Mathematics categories.
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
Contributions To Complex Analysis And Analytic Geometry
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Author : Henri Skoda
language : de
Publisher: Springer-Verlag
Release Date : 2013-08-13
Contributions To Complex Analysis And Analytic Geometry written by Henri Skoda and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.
Complex Analytic Geometry
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Author : Seymour Schuster
language : en
Publisher:
Release Date : 1949
Complex Analytic Geometry written by Seymour Schuster and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1949 with categories.
Local Analytic Geometry
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Author : Shreeram Shankar Abhyankar
language : en
Publisher: World Scientific
Release Date : 2001-01-15
Local Analytic Geometry written by Shreeram Shankar Abhyankar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-15 with Mathematics categories.
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory.The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from number theory. When it is specialized to the complex case, connectivity and other topological properties come to the fore. In particular, via singularities of analytic sets, topological fundamental groups can be studied.In the transition from punctual to local, i.e. from properties at a point to properties near a point, the classical work of Osgood plays an important role. This gives rise to normic forms and the concept of the Osgoodian. Following Serre, the passage from local to global properties of analytic spaces is facilitated by introducing sheaf theory. Here the fundamental results are the coherence theorems of Oka and Cartan. They are followed by theory normalization due to Oka and Zariski in the analytic and algebraic cases, respectively.
Complex Analytic Geometry
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Author : Gabriele Fischer
language : en
Publisher:
Release Date : 2014-09-01
Complex Analytic Geometry written by Gabriele Fischer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
