Complex Geometry: An Introduction (Universitext) 2005th Edition by Daniel Huybrechts (PDF)

Description

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

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excellent introduction to complex geometry. Coming from differential geometry, I was surprised how different the methods of complex geometry are. In particular, there is a large overlap with algebraic geometry; as a consequence of the much stronger assumption on a manifold having a holomorphic atlas most complex manifolds are given by zeros of polynomials. Therefore you will need a solid grasp of the basic ideas of algebraic geometry, for example in Vakil’s FOAG notes. Besides that, it was a bit disappointing that Huybrechts does not prove Hirzebruch-Riemann Roch, you will have to find it elsewhere. Otherwise, great book. Huybrechts is a clear writer, and there are several good exercises.

⭐I have never had a course on complex analysis, nor on complex geometry. All my knowledge in Geometry and Analysis came from the “Real” world. Nevertheless, I started studying by my own and found this text very interesting. Using it side-by-side with Nakahara’s book, I had a good balance between the necessary formalism (Huybrecht’s book) and the main topics and intuition (Nakahara’s book).

⭐This book is an excellent introduction to the marvellous world of complex geometry. The proofs are very detail so the newcomers to this field will find it very useful. The background needed to read this book is just basic grad. courses in algebra, complex analysis and smooth manifolds. This book has 2 special features that makes it very attractive:i)This book covers in detail and with clear explanations and proofs all the “foundational material” presented in chapter 0 of Harris & Griffiths Principles of algebraic geometry, this is very convenient for the newcomer as chapter 0 in Harris & Griffith provides just brief and rough sketches and comments of fundamental concepts and proofs making chapter 0 not a very good place to learn many fundamental results and concepts that have to be mastered by any serious beginner in complex geometry.ii)Chapter 6 provides a very clear and lucid introduction to deformation of complex structures. The standard references for this topic are the classical Kodaira’s books: Complex manifolds (Kodaira/Morrow) and Complex manifolds and deformations of complex structures (Kodaira 1985). These books are systematic and comprehensive therefore it may not be easy to get started using them, however Chapter 6 provides and clear overview of the topics covered in these books and as far as I know this is the only textbook where you can find an introduction to deformation of complex structures.Huybrechts provides a systematic introduction to complex geometry, with a lot of details and comments, excellent for the beginner. However if you are interested in reaching as fast as possible topics such as Calabi-Yau manifolds, Kahler-Einstein metrics, K3 surfaces, hyperkahler manifolds, G2-metrics etc., I recommend the more concise book: Lectures on Kähler Geometry by Andrei Moroianu,this is the most efficient vehicle you can use to reach quickly modern research topics; you can use Huybrechts’ book as an excellent supplement to find more examples and explanations and reach quickly advance topics in complex differential geometry.

⭐Do not buy it from here. The quality of the print is horrible. My printer makes a better print from the file than this seller! Someone has printed this book locally with low toner!

⭐very well written og good print.

⭐This book is an excellent introduction to the marvellous world of complex geometry. The proofs are very detail so the newcomers to this field will find it very useful. The background needed to read this book is just basic grad. courses in algebra, complex analysis and smooth manifolds. This book has 2 special features that makes it very attractive:i)This book covers in detail and with clear explanations and proofs all the “foundational material” presented in chapter 0 of Harris & Griffiths Principles of algebraic geometry, this is very convenient for the newcomer as chapter 0 in Harris & Griffith provides just brief and rough sketches and comments of fundamental concepts and proofs making chapter 0 not a very good place to learn many fundamental results and concepts that have to be mastered by any serious beginner in complex geometry.ii)Chapter 6 provides a very clear and lucid introduction to deformation of complex structures. The standard references for this topic are the classical Kodaira’s books: Complex manifolds (Kodaira/Morrow) and Complex manifolds and deformations of complex structures (Kodaira 1985). These books are systematic and comprehensive therefore it may not be easy to get started using them, however Chapter 6 provides and clear overview of the topics covered in these books and as far as I know this is the only textbook where you can find an introduction to deformation of complex structures.Huybrechts provides a systematic introduction to complex geometry, with a lot of details and comments, excellent for the beginner. However if you are interested in reaching as fast as possible topics such as Calabi-Yau manifolds, Kahler-Einstein metrics, K3 surfaces, hyperkahler manifolds, G2-metrics etc., I recommend the more concise book: Lectures on Kähler Geometry by Andrei Moroianu,this is the most efficient vehicle you can use to reach quickly modern research topics; you can use Huybrechts’ book as an excellent supplement to find more examples and explanations and reach quickly advance topics in complex differential geometry.

⭐Complete introduction to a tough but interesting field of study

⭐Esperaba que fuera más ameno, voy a sufrir con esta lectura.

⭐Not found.

⭐C’est une excellente introduction au sujet et qui contient aussi des chapitres vraiment avancés. Pour se lancer dedans il est nécessaire de connaître un minimum d’analyse complexe à une variable et de géométrie différentielle réelle mais c’est tout, ensuite on peut très bien en profiter sans connaître de géométrie algébrique. Et les sujets traités à la fin et dans les annexes sont nettement plus avancés, tout en restant écrits de façon bien plus accessible que d’autres références comme le livre de Voisin.

⭐Not found.

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