Top 10 recommendation complex manifolds 2019
When you looking for complex manifolds, you must consider not only the quality but also price and customer reviews. But among hundreds of product with different price range, choosing suitable complex manifolds is not an easy task. In this post, we show you how to find the right complex manifolds along with our top-rated reviews. Please check out our suggestions to find the best complex manifolds for you.
Best complex manifolds
1. Differential Analysis on Complex Manifolds (Graduate Texts in Mathematics)
Description
A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wellss superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Pradas appendix gives an overview of the developments in the field during the decades since the book appeared.
2. Complex Manifolds (AMS Chelsea Publishing)
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Used Book in Good ConditionDescription
This volume serves as an introduction to the Kodaira-Spencer theory of deformations of complex structures. Based on notes taken by James Morrow from lectures given by Kunihiko Kodaira at Stanford University in 1965-1966, the book gives the original proof of the Kodaira embedding theorem, showing that the restricted class of Khler manifolds called Hodge manifolds is algebraic. Included are the semicontinuity theorems and the local completeness theorem of Kuranishi. Readers are assumed to know some algebraic topology. Complete references are given for the results that are used from elliptic partial differential equations. The book is suitable for graduate students and researchers interested in abstract complex manifolds.3. From Holomorphic Functions to Complex Manifolds (Graduate Texts in Mathematics)
Description
This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.
4. Complex Geometry: An Introduction (Universitext)
Description
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)
5. Complex Manifolds without Potential Theory: with an appendix on the geometry of characteristic classes (Universitext)
Description
From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress....The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#
6. Basic Algebraic Geometry 2: Schemes and Complex Manifolds
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SpringerDescription
Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevichs book is a must.''
The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Khler geometry and Hodge theory. The final section raisesan important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''.
The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.
7. Analysis on Real and Complex Manifolds, Volume 35 (North-Holland Mathematical Library)
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North-HollandDescription
Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem.
The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincar and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem.
Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein.
8. Complex Manifolds and Deformation of Complex Structures (Classics in Mathematics)
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Used Book in Good ConditionDescription
Kodairais a Fields Medal Prize Winner. (In the absence of a Nobel prize in mathematics, they are regarded as the highest professional honour a mathematician can attain.)
Kodaira is an honorary member of the London Mathematical Society.
Affordable softcover edition of 1986 classic
9. Several Complex Variables and Complex Manifolds II (London Mathematical Society Lecture Note Series) (Pt.2)
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Used Book in Good ConditionDescription
This self-contained and relatively elementary introduction to functions of several complex variables and complex (especially compact) manifolds is intended to be a synthesis of those topics and a broad introduction to the field. Part I is suitable for advanced undergraduates and beginning postgraduates whilst Part II is written more for the graduate student. The work as a whole will be useful to professional mathematicians or mathematical physicists who wish to acquire a working knowledge of this area of mathematics. Many exercises have been included and indeed they form an integral part of the text. The prerequisites for understanding Part I would be met by any mathematics student with a first degree and together the two parts provide an introduction to the more advanced works in the subject.10. Complex Manifolds
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