Complex Geometry: An IntroductionSpringer Science & Business Media, 02.09.2005 - 314 Seiten 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. |
Inhalt
| 1 | |
| 51 | |
Kähler Manifolds | 113 |
Vector Bundles | 165 |
Applications of Cohomology 231 | 230 |
Deformations of Complex Structures | 255 |
A Hodge Theory on Differentiable Manifolds | 281 |
B Sheaf Cohomology | 287 |
References | 297 |
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Häufige Begriffe und Wortgruppen
analytic arbitrary assertion bijective blow-up C-linear canonical Chern classes Chern connection cocycle compact complex manifold compact Kähler manifold complex manifold complex structure complex torus complex vector bundle Corollary curve defined Definition deformation denote differentiable manifold direct sum Div(X divisor End(E endowed equation Example Exercise exists Əzi fact fibre formula function ƒ fundamental form geometry given H¹(X Hence Hermite-Einstein hermitian manifold hermitian structure Hodge structure holomorphic function holomorphic line bundle holomorphic map holomorphic vector bundle hypersurface integral irreducible isomorphic Kähler class Kähler form Kähler metric Kähler structure Kähler-Einstein Kodaira Lefschetz operator Lemma linear meromorphic function metric g natural non-trivial open covering open subset Pic(X Proof Proposition prove pull-back quotient respect Riemannian manifold sheaf sheaves short exact sequence Show submanifold surjective theorem theory trivial vanishing vector space w₁ yields