Hodge Theory and Complex Algebraic Geometry I: Volume 1 (Cambridge Studies in Advanced Mathematics Book 76) 1st Edition by Claire Voisin (PDF)

Description

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

User’s Reviews

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

⭐The first volume of a treatise on Hodge Theory. It is a bit specialized, and if you don’t understand the title then this book is not for youl. If you do understand the title then you need look no further than the author.

⭐Great book and is an excellent reference work.

⭐Excellent book!

⭐The idea of Kahler space is between the best results of the modern geometry, being applied particularly to quantum physics. So we can return to traditions of this matter, considering the law of physics called “Ricci-Einstein”. It is important an ease approach , also if the Hodge method is still sufficiently complex. But Voisin offers a theory with a good language for that.

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