Rational Curves on Algebraic Varieties

1. Front Matter

   Pages I-VIII

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2. Introduction

   • János Kollár

   Pages 1-4

3. Hilbert Schemes and Chow Varieties

   • János Kollár

   Pages 5-89

4. Curves on Varieties

   • János Kollár

   Pages 90-158

5. The Cone Theorem and Minimal Models

   • János Kollár

   Pages 159-178

6. Rationally Connected Varieties

   • János Kollár

   Pages 179-237

7. Fano Varieties

   • János Kollár

   Pages 238-284

8. Appendix

   • János Kollár

   Pages 285-307

9. Back Matter

   Pages 308-321

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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.

• Chow Varietäten
• Fano Varietäten
• Fano varieties
• Hilbert schemes
• Hilbertschemata
• Kegel von Kurven
• algebraic varieties
• chow varieties
• cone of curves
• rational connected varieties
• rational verknüpfte Varietäten
• uniruled varieties

• Department of Mathematics, Princeton University, Princeton, USA

  János Kollár

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