Holomorphic Vector Bundles Over Compact Complex Surfaces
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Holomorphic Vector Bundles Over Compact Complex Surfaces
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Author : Vasile Brinzanescu
language : en
Publisher: Springer
Release Date : 2006-11-14
Holomorphic Vector Bundles Over Compact Complex Surfaces written by Vasile Brinzanescu 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.
The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector bundles and stability with respect to a Gauduchon metric, are considered. The reader requires a grounding in geometry at graduate student level. The book will be of interest to graduate students and researchers in complex, algebraic and differential geometry.
Holomorphic Vector Bundles Over Compact Complex Surfaces
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Author : Vasile Brînzănescu
language : en
Publisher:
Release Date : 1996
Holomorphic Vector Bundles Over Compact Complex Surfaces written by Vasile Brînzănescu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Lectures On Vector Bundles Over Riemann Surfaces
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Author : Robert C. Gunning
language : en
Publisher: Princeton University Press
Release Date : 1967-11-21
Lectures On Vector Bundles Over Riemann Surfaces written by Robert C. Gunning and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967-11-21 with Mathematics categories.
The description for this book, Lectures on Vector Bundles over Riemann Surfaces. (MN-6), Volume 6, will be forthcoming.
The Kobayashi Hitchin Correspondence
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Author : Martin Lubke
language : en
Publisher: World Scientific
Release Date : 1995-09-30
The Kobayashi Hitchin Correspondence written by Martin Lubke and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-30 with Mathematics categories.
By the Kobayashi-Hitchin correspondence, the authors of this book mean the isomorphy of the moduli spaces Mst of stable holomorphic — resp. MHE of irreducible Hermitian-Einstein — structures in a differentiable complex vector bundle on a compact complex manifold. They give a complete proof of this result in the most general setting, and treat several applications and some new examples.After discussing the stability concept on arbitrary compact complex manifolds in Chapter 1, the authors consider, in Chapter 2, Hermitian-Einstein structures and prove the stability of irreducible Hermitian-Einstein bundles. This implies the existence of a natural map I from MHE to Mst which is bijective by the result of (the rather technical) Chapter 3. In Chapter 4 the moduli spaces involved are studied in detail, in particular it is shown that their natural analytic structures are isomorphic via I. Also a comparison theorem for moduli spaces of instantons resp. stable bundles is proved; this is the form in which the Kobayashi-Hitchin has been used in Donaldson theory to study differentiable structures of complex surfaces. The fact that I is an isomorphism of real analytic spaces is applied in Chapter 5 to show the openness of the stability condition and the existence of a natural Hermitian metric in the moduli space, and to study, at least in some cases, the dependence of Mst on the base metric used to define stability. Another application is a rather simple proof of Bogomolov's theorem on surfaces of type VII0. In Chapter 6, some moduli spaces of stable bundles are calculated to illustrate what can happen in the general (i.e. not necessarily Kähler) case compared to the algebraic or Kähler one. Finally, appendices containing results, especially from Hermitian geometry and analysis, in the form they are used in the main part of the book are included.
An Introduction To Families Deformations And Moduli
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Author : Thiruvalloor E. Venkata Balaji
language : en
Publisher: Universitätsverlag Göttingen
Release Date : 2010
An Introduction To Families Deformations And Moduli written by Thiruvalloor E. Venkata Balaji and has been published by Universitätsverlag Göttingen this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Complex manifolds categories.
Moduli Theory is one of those areas of Mathematics that has fascinated minds from classical to modern times. This has been so because it reveals beautiful Geometry naturally hidden in questions involving classification of geometric objects and because of the profound use of the methods of several areas of Mathematics like Algebra, Number Theory, Topology and Analysis to achieve this revelation. A study of Moduli Theory would therefore give senior undergraduate and graduate students an integrated view of Mathematics. The present book is a humble introduction to some aspects of Moduli Theory.
Mathematical Works
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Author : Erich Kähler
language : en
Publisher: Walter de Gruyter
Release Date : 2003
Mathematical Works written by Erich Kähler and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
For most mathematicians and many mathematical physicists the name Erich Kähler is strongly tied to important geometric notions such as Kähler metrics, Kähler manifolds and Kähler groups. They all go back to a paper of 14 pages written in 1932. This, however, is just a small part of Kähler's many outstanding achievements which cover an unusually wide area: From celestial mechanics he got into complex function theory, differential equations, analytic and complex geometry with differential forms, and then into his main topic, i.e. arithmetic geometry where he constructed a system of notions which is a precursor and, in large parts, equivalent to the now used system of Grothendieck and Dieudonné. His principal interest was in finding the unity in the variety of mathematical themes and establishing thus mathematics as a universal language. In this volume Kähler's mathematical papers are collected following a "Tribute to Herrn Erich Kähler" by S. S. Chern, an overview of Kähler's life data by A. Bohm and R. Berndt, and a Survey of his Mathematical Work by the editors. There are also comments and reports on the developments of the main topics of Kähler's work, starting by W. Neumann's paper on the topology of hypersurface singularities, J.-P. Bourguignon's report on Kähler geometry and, among others by Berndt, Bost, Deitmar, Ekeland, Kunz and Krieg, up to A. Nicolai's essay "Supersymmetry, Kähler geometry and Beyond". As Kähler's interest went beyond the realm of mathematics and mathematical physics, any picture of his work would be incomplete without touching his work reaching into other regions. So a short appendix reproduces three of his articles concerning his vision of mathematics as a universal Theme together with an essay by K. Maurin giving an "Approach to the philosophy of Erich Kähler".
The Riemann Boundary Problem On Riemann Surfaces
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Author : Y. Rodin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
The Riemann Boundary Problem On Riemann Surfaces written by Y. Rodin 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.
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Analysis Complex Geometry And Mathematical Physics
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Author : Paul M. N. Feehan
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-07-21
Analysis Complex Geometry And Mathematical Physics written by Paul M. N. Feehan 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 2015-07-21 with Mathematics categories.
This volume contains the proceedings of the Conference on Analysis, Complex Geometry and Mathematical Physics: In Honor of Duong H. Phong, which was held from May 7-11, 2013, at Columbia University, New York. The conference featured thirty speakers who spoke on a range of topics reflecting the breadth and depth of the research interests of Duong H. Phong on the occasion of his sixtieth birthday. A common thread, familiar from Phong's own work, was the focus on the interplay between the deep tools of analysis and the rich structures of geometry and physics. Papers included in this volume cover topics such as the complex Monge-Ampère equation, pluripotential theory, geometric partial differential equations, theories of integral operators, integrable systems and perturbative superstring theory.
Differentiability Of Six Operators On Nonsmooth Functions And P Variation
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Author : R. M. Dudley
language : en
Publisher: Springer
Release Date : 2006-12-08
Differentiability Of Six Operators On Nonsmooth Functions And P Variation written by R. M. Dudley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.
Smooth Four Manifolds And Complex Surfaces
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Author : Robert Friedman
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-03-10
Smooth Four Manifolds And Complex Surfaces written by Robert Friedman 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 1994-03-10 with Mathematics categories.
In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.