The aim of this monograph is to give a comprehensive introduction to the structure theory of higher dimensional algebraic varieties by studying the geometry of curves, especially rational curves, on them. The book contains many exercises which makes it especially suitable as a graduate level textbook.

Includes supplementary material: sn.pub/extras

Inhalt
I. Hilbert Schemes and Chow Varieties.- II. Curves on Varieties.- III. The Cone Theorem and Minimal Models.- IV. Rationally Connected Varieties.- V. Fano Varieties.- VI. Appendix.- References.