Im Sortiment seit:
Ergebnisse der Mathematik und ihrer Grenzgebiete (Nr. 32)
The aim of this book is to provide an introduction to the structure theory of higher dimensional algebraic varieties by studying the geometry of curves, especially rational curves, on varieties. The main applications are in the study of Fano varieties and of related varieties with lots of rational curves on them. This Ergebnisse volume provides the first systematic introduction to this field of study. The book contains a large number of examples and exercises which serve to illustrate the range of the methods and also lead to many open questions of current research.
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.
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.