Complex Geometry: An Introduction (Universitext)

Daniel Huybrechts

Softcover

ISBN 10: 3540212906 ISBN 13: 9783540212904

Publisher: Springer, 2004

Easily accessible

Includes recent developments

Assumes very little knowledge of differentiable manifolds and functional analysis

Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Review:

"This is the book that a generation of complex geometers will wish had existed when they first learned the subject, and that the next generation of geometers will surely use. ... Inserted into the standard material are some excellent appendices to stimulate interest and further reading ... . the reader learning the basic material is brought quickly and often to some fascinating areas of current research. Exercises introduce many examples ... . The result is an excellent course in complex geometry." --Richard P. Thomas, Mathematical Reviews, 2005h

"The book is based on a year course on complex geometry and its interaction with Riemannian geometry. It prepares a basic ground for a study of complex geometry as well as for understanding ideas coming recently from string theory. ... The book is a very good introduction to the subject and can be very useful both for mathematicians and mathematical physicists." --EMS Newsletter, June, 2005

Synopsis:

"Complex Geometry" studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in string theory have made it an highly attractive area, both for mathematicians and theoretical physicists. The author's goal is to provide an easily accessible introduction to the subject. The book contains detailed accounts of the basic concepts and the many exercises illustrate the theory. The appendices to various chapters allow an outlook to recent research directions. Daniel Huybrechts is currently Professor of Mathematics at the University Denis Diderot in Paris.