## Zur Klassifikationstheorie drei (und höher) dimensionaler projektiver Mannigfaltigkeiten.(German)Zbl 0546.14025

This survey is supposed to serve as an introduction to the birational classification theory of three and higher dimensional projective manifolds. The ”state of art” and several ”standard conjectures” are discussed. More recent developments, due to Y. Kawamata, are: A numerical criterion saying, whether the canonical sheaf of a canonical model is semiample or not. A proof of $$C^+_{n,m}$$ for fibre-spaces whose general fibre has a canonical model with a semiample canonical sheaf.

### MSC:

 14J10 Families, moduli, classification: algebraic theory 14E30 Minimal model program (Mori theory, extremal rays) 14J30 $$3$$-folds 14J15 Moduli, classification: analytic theory; relations with modular forms 32J25 Transcendental methods of algebraic geometry (complex-analytic aspects) 14D99 Families, fibrations in algebraic geometry