COMPLEX GEOMETRY HUYBRECHTS PDF

Post-doctorial positions at Inst. Professor: Cologne , Paris since Having been designed for third-year students, the aim of the course was to acquaint beginners in the field with some basic concepts, fundamental techniques, and important results in the theory of compact complex manifolds, without being neither too basic nor too sketchy. Also, as complex geometry has undergone tremendous developments during the past five decades, and become an indispensable framework in modern mathematical physics, the author has tried to teach the subject in such a way that would enable the students to understand the more recent developments in the field, too, up to some of the fascinating aspects of the stunning interplay between complex geometry and quantum field theory in theoretical physics. As to the precise contents, the text consists of six chapters and two appendices. Those are meant to help the unexperienced reader to recall a few basic concepts and facts from differential geometry, Hodge theory on differentiable manifolds, sheaf theory, and sheaf cohomology.

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Post-doctorial positions at Inst. Professor: Cologne , Paris since Inhaltsangabe Local Theory. Having been designed for third-year students, the aim of the course was to acquaint beginners in the field with some basic concepts, fundamental techniques, and important results in the theory of compact complex manifolds, without being neither too basic nor too sketchy.

Also, as complex geometry has undergone tremendous developments during the past five decades, and become an indispensable framework in modern mathematical physics, the author has tried to teach the subject in such a way that would enable the students to understand the more recent developments in the field, too, up to some of the fascinating aspects of the stunning interplay between complex geometry and quantum field theory in theoretical physics.

As to the precise contents, the text consists of six chapters and two appendices. Those are meant to help the unexperienced reader to recall a few basic concepts and facts from differential geometry, Hodge theory on differentiable manifolds, sheaf theory, and sheaf cohomology. This very user-friendly service makes the entire introductory text more comfortable for less seasoned students, perhaps also for interested and mathematically less experienced physicists, although the author does not claim absolute self-containedness of the book.

The entire text comes with a wealth of enlightening examples, historical remarks, comments and hints for further reading, outlooks to other directions of research, and numerous exercises after each section. The exercises are far from being bland and often quite demanding, but they should be mastered by ambitious and attentive readers, in the last resort after additional reading.

Finally, there is a very rich bibliography of references, also from the very recent research literature, which the author profusely refers to throughout the entire text. The whole exposition captivates by its clarity, profundity, versality, and didactical strategy, which lead the reader right to the more advanced literature in complex geometry as well as to the forefront of research in geometry and its applications to mathematical physics.

No doubt, this book is an outstanding introduction to modern complex geometry. It provides a clear and deep introduction about complex geometry, namely the study of complex manifolds. These are differentiable manifolds endowed with the additional datum of a complex structure that is more rigid than the geometrical structures used in differential geometry.

Complex geometry is on the crossroad of algebraic and differential geometry. Complex geometry is also becoming a stimulating and useful tool for theoretical physicists working in string theory and conformal field theory.

The physicist, will be very glad to discover the interplay between complex geometry and supersymmetry and mirror symmetry. The book begins by explaining the local theory and all you need to understand the global structure of complex manifolds.

Then we get an introduction to the complex manifolds as such, where the reader can progressively perceive the difference between real manifolds and complex ones. And the physicist will be glad to find therein a first step on the road going from complex geometry to conformal field theory and supersymmetry.

One chapter is dedicated to the study of holomorphic vector bundles connections, curvature, Chern classes. With all this stuff it is then possible to focus on some applications of cohomology. This leads to a nice introduction to the famous Hirzebruch-Riemann-Roch theorem and to Kodaira vanishing and embedding theorems. The last chapter of the book tackles the very important topics of deformations of complex structures. This chapter will be interesting especially for readers that are studying Calabi-Yau manifolds and mirror symmetries.

The main text of the book is completed by two pedagogical appendices. One about Hodge theory and the other about sheaf cohomology. Thus this beautiful textbook will be very interesting for both pure mathematicians and theoretical physicists working in recent domains of field theory. It can be used by students or scientists for a first introduction in this field. It is always very accessible and the reader will find a detailed account of the basic concepts and many well-chosen exercises that illustrate the theory.

Many illuminating examples help the reader in the understanding of all fundamental notions. I could certainly recommend this textbook to my students attending my lectures on differential geometry. This very user-friendly The entire text comes with a wealth of enlightening examples, historical remarks, comments and hints Finally, there is a very rich bibliography The whole exposition captivates by its clarity, profundity, versality, and didactical strategy Appendices to various chapters allow an outlook to recent research directions.

Inserted into the standard material are some excellent appendices to stimulate interest and further reading Exercises introduce many examples The result is an excellent course in complex geometry. Thomas, Mathematical Reviews, h "The book is based on a year course on complex geometry and its interaction with Riemannian geometry. It prepares a basic ground for a study of complex geometry as well as for understanding ideas coming recently from string theory.

The book is a very good introduction to the subject and can be very useful both for mathematicians and mathematical physicists.

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Post-doctorial positions at Inst. Professor: Cologne , Paris since Inhaltsangabe Local Theory. Having been designed for third-year students, the aim of the course was to acquaint beginners in the field with some basic concepts, fundamental techniques, and important results in the theory of compact complex manifolds, without being neither too basic nor too sketchy.

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