Lectures on Kähler Geometry

Kähler geometry is of substantial interest to both mathematicians and physicists and this graduate text provides a self-contained introduction to the subject. Topics discussed include complex manifolds and holomorphic vector bundles; Kähler manifolds and Hodge and Dolbeault theories; compact Kähler manifolds and a proof of the famous Kähler identities.

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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.