TY  - BOOK
AU  - Lee,John M.
TI  - Introduction to complex manifolds
T2  - Graduate studies in mathematics
SN  - 9781470477820
U1  - 515.946 23
PY  - 2024///
CY  - Providence, Rhode Island
PB  - American Mathematical Society
KW  - Complex manifolds
KW  - Differential geometry
KW  - Complex analysis
KW  - Kähler manifolds
KW  - Algebraic geometry
N1  - Includes bibliographical references and index; The basics -- Complex submanifolds -- Holomorphic vector bundles -- The Dolbeault complex -- Sheaves -- Sheaf cohomology -- Connections -- Hermitian and Kähler manifolds -- Hodge theory -- The Kodaira embedding theorem
N2  - This graduate-level textbook provides a comprehensive introduction to the theory of complex manifolds from the perspective of differential geometry. Beginning with the foundations of smooth and complex manifolds, the book develops the essential concepts, techniques, and structures used in modern complex geometry, including holomorphic maps, complex submanifolds, vector bundles, Dolbeault cohomology, sheaf theory, Hermitian and Kähler geometry, Hodge theory, and the Kodaira embedding theorem. Emphasizing intuition together with mathematical rigor, the author explains how analytic, topological, and geometric ideas interact in the study of complex manifolds. Numerous examples, exercises, and detailed proofs make the text suitable for graduate students and researchers seeking an accessible yet advanced treatment of complex geometry and its applications in differential geometry, algebraic geometry, topology, and mathematical physics
ER  -