Cohomological Aspects In Complex Non Kahler Geometry

Author : Daniele Angella
Publisher : Springer
Page : 289 pages
File Size : 51,6 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9783319024417

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Cohomological Aspects in Complex Non-Kähler Geometry by Daniele Angella Pdf

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kähler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kähler structure. We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered.

Author : Daniele Angella
Publisher : Unknown
Page : 292 pages
File Size : 50,8 Mb
Release : 2013-12-31
Category : Electronic
ISBN : 3319024426

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Cohomological Aspects in Complex Non-Kahler Geometry by Daniele Angella Pdf

Author : Daniele Angella,Costantino Medori,Adriano Tomassini
Publisher : Springer
Page : 262 pages
File Size : 43,6 Mb
Release : 2017-10-12
Category : Mathematics
ISBN : 9783319629148

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Complex and Symplectic Geometry by Daniele Angella,Costantino Medori,Adriano Tomassini Pdf

This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Author : Ilarion V. Melnikov
Publisher : Springer
Page : 482 pages
File Size : 51,6 Mb
Release : 2019-02-11
Category : Science
ISBN : 9783030050856

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An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry by Ilarion V. Melnikov Pdf

This book introduces two-dimensional supersymmetric field theories with emphasis on both linear and non-linear sigma models. Complex differential geometry, in connection with supersymmetry, has played a key role in most developments of the last thirty years in quantum field theory and string theory. Both structures introduce a great deal of rigidity compared to the more general categories of non-supersymmetric theories and real differential geometry, allowing for many general conceptual results and detailed quantitative predictions. Two-dimensional (0,2) supersymmetric quantum field theories provide a natural arena for the fruitful interplay between geometry and quantum field theory. These theories play an important role in string theory and provide generalizations, still to be explored fully, of rich structures such as mirror symmetry. They also have applications to non-perturbative four-dimensional physics, for instance as descriptions of surface defects or low energy dynamics of solitonic strings in four-dimensional supersymmetric theories. The purpose of these lecture notes is to acquaint the reader with these fascinating theories, assuming a background in conformal theory, quantum field theory and differential geometry at the beginning graduate level. In order to investigate the profound relations between structures from complex geometry and field theory the text begins with a thorough examination of the basic structures of (0,2) quantum field theory and conformal field theory. Next, a simple class of Lagrangian theories, the (0,2) Landau-Ginzburg models, are discussed, together with the resulting renormalization group flows, dynamics, and symmetries. After a thorough introduction and examination of (0,2) non-linear sigma models, the text introduces linear sigma models that, in particular, provide a unified treatment of non-linear sigma models and Landau-Ginzburg theories. Many exercises, along with discussions of relevant mathematical notions and important open problems in the field, are included in the text.

Author : Akito Futaki,Reiko Miyaoka,Zizhou Tang,Weiping Zhang
Publisher : Springer
Page : 348 pages
File Size : 53,5 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9784431560210

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Geometry and Topology of Manifolds by Akito Futaki,Reiko Miyaoka,Zizhou Tang,Weiping Zhang Pdf

Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists.The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, symplectic and contact geometry, and complex geometry.

Author : Liviu Ornea,Misha Verbitsky
Publisher : Birkhäuser
Page : 0 pages
File Size : 46,9 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 3031581199

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Principles of Locally Conformally Kähler Geometry by Liviu Ornea,Misha Verbitsky Pdf

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.

Author : Sławomir Dinew,Sebastien Picard,Andrei Teleman,Alberto Verjovsky
Publisher : Springer Nature
Page : 242 pages
File Size : 55,6 Mb
Release : 2019-11-05
Category : Mathematics
ISBN : 9783030258832

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Complex Non-Kähler Geometry by Sławomir Dinew,Sebastien Picard,Andrei Teleman,Alberto Verjovsky Pdf

Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds. The school consisted of four courses, focusing on both the construction of non-Kähler manifolds and the understanding of a possible classification of complex non-Kähler manifolds. In particular, the courses by Alberto Verjovsky and Andrei Teleman introduced tools in the theory of foliations and analytic techniques for the classification of compact complex surfaces and compact Kähler manifolds, respectively. The courses by Sebastien Picard and Sławomir Dinew focused on analytic techniques in Hermitian geometry, more precisely, on special Hermitian metrics and geometric flows, and on pluripotential theory in complex non-Kähler geometry.

Author : Alesky Tralle,John Oprea
Publisher : Springer
Page : 216 pages
File Size : 42,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540691457

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Symplectic Manifolds with no Kaehler structure by Alesky Tralle,John Oprea Pdf

This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory. In recent years, some new and stimulating conjectures and problems have been formulated due to an influx of homotopical ideas. Examples include the Lupton-Oprea conjecture, the Benson-Gordon conjecture, both of which are in the spirit of some older and still unsolved problems (e.g. Thurston's conjecture and Sullivan's problem). Our explicit aim is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory in the framework of the problems mentioned above. We expect that the reader is aware of the basics of differential geometry and algebraic topology at graduate level.

Author : Fabrizio Catanese,Hélène Esnault,Alan Huckleberry,Klaus Hulek,Thomas Peternell
Publisher : Springer
Page : 0 pages
File Size : 41,5 Mb
Release : 2010-10-14
Category : Mathematics
ISBN : 3642071317

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Global Aspects of Complex Geometry by Fabrizio Catanese,Hélène Esnault,Alan Huckleberry,Klaus Hulek,Thomas Peternell Pdf

This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kähler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry

Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 55,5 Mb
Release : 2005
Category : Computers
ISBN : 3540212906

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Complex Geometry by Daniel Huybrechts Pdf

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Author : Fabrizio Catanese,Hélène Esnault,Alan Huckleberry,Klaus Hulek,Thomas Peternell
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 48,8 Mb
Release : 2006-09-29
Category : Mathematics
ISBN : 9783540354802

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Global Aspects of Complex Geometry by Fabrizio Catanese,Hélène Esnault,Alan Huckleberry,Klaus Hulek,Thomas Peternell Pdf

This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kähler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry

Author : Simon G. Chiossi,Anna Fino,Emilio Musso,Fabio Podestà,Luigi Vezzoni
Publisher : Springer
Page : 338 pages
File Size : 45,8 Mb
Release : 2017-11-27
Category : Mathematics
ISBN : 9783319675190

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Special Metrics and Group Actions in Geometry by Simon G. Chiossi,Anna Fino,Emilio Musso,Fabio Podestà,Luigi Vezzoni Pdf

The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

Author : Andrei Moroianu
Publisher : Cambridge University Press
Page : 4 pages
File Size : 43,6 Mb
Release : 2007-03-29
Category : Mathematics
ISBN : 9781139463003

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Lectures on Kähler Geometry by Andrei Moroianu Pdf

Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.

Author : Jean H. Gallier,Jocelyn Quaintance
Publisher : Unknown
Page : 0 pages
File Size : 46,7 Mb
Release : 2022
Category : Algebraic topology
ISBN : 9811245037

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Homology, Cohomology, and Sheaf Cohomology for Algebraic Topology, Algebraic Geometry, and Differential Geometry by Jean H. Gallier,Jocelyn Quaintance Pdf

"For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts"--

Author : Anonim
Publisher : Unknown
Page : 796 pages
File Size : 51,9 Mb
Release : 2006
Category : Mathematics
ISBN : UOM:39015067268402

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Mathematical Reviews by Anonim Pdf