Holomorphic Vector Bundles On Non Algebraic Surfaces
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Algebraic Surfaces And Holomorphic Vector Bundles
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Author : Robert Friedman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Surfaces And Holomorphic Vector Bundles 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 2012-12-06 with Mathematics categories.
This book is based on courses given at Columbia University on vector bun dles (1988) and on the theory of algebraic surfaces (1992), as well as lectures in the Park City lIAS Mathematics Institute on 4-manifolds and Donald son invariants. The goal of these lectures was to acquaint researchers in 4-manifold topology with the classification of algebraic surfaces and with methods for describing moduli spaces of holomorphic bundles on algebraic surfaces with a view toward computing Donaldson invariants. Since that time, the focus of 4-manifold topology has shifted dramatically, at first be cause topological methods have largely superseded algebro-geometric meth ods in computing Donaldson invariants, and more importantly because of and Witten, which have greatly sim the new invariants defined by Seiberg plified the theory and led to proofs of the basic conjectures concerning the 4-manifold topology of algebraic surfaces. However, the study of algebraic surfaces and the moduli spaces ofbundles on them remains a fundamen tal problem in algebraic geometry, and I hope that this book will make this subject more accessible. Moreover, the recent applications of Seiberg Witten theory to symplectic 4-manifolds suggest that there is room for yet another treatment of the classification of algebraic surfaces. In particular, despite the number of excellent books concerning algebraic surfaces, I hope that the half of this book devoted to them will serve as an introduction to the subject.
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 On Non Algebraic Surfaces
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Author : Matei Toma
language : en
Publisher:
Release Date : 1992
Holomorphic Vector Bundles On Non Algebraic Surfaces written by Matei Toma and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Proceedings Of The International Conference On Complex Geometry And Related Fields
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Author : Zhijie Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Proceedings Of The International Conference On Complex Geometry And Related Fields written by Zhijie Chen 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 2007 with Mathematics categories.
In commemoration and celebration of the tenth anniversary of the Institute of Mathematics at East China Normal University, an International Conference on complex geometry and related fields recently convened. This collection presents some of the conference highlights, dealing with various and significant topics of differential and algebraic geometry, while exploring their connections to number theory and mathematical physics. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.
Geometric Invariant Theory Holomorphic Vector Bundles And The Harder Narasimhan Filtration
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Author : Alfonso Zamora Saiz
language : en
Publisher: Springer Nature
Release Date : 2021-03-24
Geometric Invariant Theory Holomorphic Vector Bundles And The Harder Narasimhan Filtration written by Alfonso Zamora Saiz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-24 with Mathematics categories.
This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Gauge Theory And The Topology Of Four Manifolds
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Author : Robert Friedman
language : en
Publisher: American Mathematical Society, IAS/Park City Mathematics Institute
Release Date : 2024-12-05
Gauge Theory And The Topology Of Four Manifolds written by Robert Friedman and has been published by American Mathematical Society, IAS/Park City Mathematics Institute this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-05 with Mathematics categories.
The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying $SU(2)$-gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the Seiberg-Witten theory. Gauge theory long predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space. One reason for the interest in this study is the connection between the gauge theory moduli spaces of a Kähler manifold and the algebro-geometric moduli space of stable holomorphic bundles over the manifold. The extra geometric richness of the $SU(2)$-moduli spaces may one day be important for purposes beyond the algebraic invariants that have been studied to date. It is for this reason that the results presented in this volume will be essential.
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures
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Author : Rajendra Bhatia
language : en
Publisher: World Scientific
Release Date : 2011-06-06
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures written by Rajendra Bhatia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-06 with Mathematics categories.
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Principles Of Locally Conformally K Hler Geometry
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Author : Liviu Ornea
language : en
Publisher: Springer Nature
Release Date : 2024-05-02
Principles Of Locally Conformally K Hler Geometry written by Liviu Ornea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-02 with Mathematics categories.
This monograph introduces readers to locally conformally Kähler (LCK) geometry and provides an extensive overview of the most current results. A rapidly developing area in complex geometry dealing with non-Kähler manifolds, LCK geometry has strong links to many other areas of mathematics, including algebraic geometry, topology, and complex analysis. The authors emphasize these connections to create a unified and rigorous treatment of the subject suitable for both students and researchers. Part I builds the necessary foundations for those approaching LCK geometry for the first time with full, mostly self-contained proofs and also covers material often omitted from textbooks, such as contact and Sasakian geometry, orbifolds, Ehresmann connections, and foliation theory. More advanced topics are then treated in Part II, including non-Kähler elliptic surfaces, cohomology of holomorphic vector bundles on Hopf manifolds, Kuranishi and Teichmüller spaces for LCK manifolds with potential, and harmonic forms on Sasakian and Vaisman manifolds. Each chapter in Parts I and II begins with motivation and historic context for the topics explored and includes numerous exercises for further exploration of important topics. Part III surveys the current research on LCK geometry, describing advances on topics such as automorphism groups on LCK manifolds, twisted Hamiltonian actions and LCK reduction, Einstein-Weyl manifolds and the Futaki invariant, and LCK geometry on nilmanifolds and on solvmanifolds. New proofs of many results are given using the methods developed earlier in the text. The text then concludes with a chapter that gathers over 100 open problems, with context and remarks provided where possible, to inspire future research.
The Monodromy Group
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Author : Henryk Żołądek
language : en
Publisher: Springer Nature
Release Date : 2025-05-10
The Monodromy Group written by Henryk Żołądek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-10 with Mathematics categories.
This book presents the monodromy group, underlining the unifying role it plays in a variety of theories and mathematical areas. In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. In the theory of systems of linear differential equations, one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliations, there appear the Ecalle-Voronin-Martinet-Ramis moduli. Moreover, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. Readers will quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature. This second edition has been enlarged by several sections, presenting new results appeared since the first edition.