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. 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.

Autorentext

Daniel Huybrechts is currently Professor of Mathematics at the University Denis Diderot in Paris.

Brief career details:

Studies of math at Humboldt University Berlin and Max-=Planck-Institute Bonn 1985-1992.

Post-doctorial positions at Inst. for Advanced Study Priceton, Ecole Normale Supérieure Paris, Max-Planck-Inst Bonn, University Essen, IHES Paris.

Professor: Cologne 1998-2002, Paris since 2002.

Klappentext

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)

Inhalt

Local Theory.- Complex Manifolds.- Kähler Manifolds.- Vector Bundles.- Applications of Cohomology.- Deformations of Complex Structures.