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  3. Lectures on Kähler Geometry
  • Cited by 51
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
2007
Online ISBN:
9780511618666
DOI:
https://doi.org/10.1017/CBO9780511618666
Subjects:
Mathematics (general), Mathematics, Geometry and Topology
Series:
London Mathematical Society Student Texts (69)
Information

Book description

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.

Reviews

"A concise and well-written modern introduction to the subject."
Tatyana E. Foth, Mathematical Reviews

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