Ebook: Rational Curves on Algebraic Varieties

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.

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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.

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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.
Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-4
Hilbert Schemes and Chow Varieties....Pages 5-89
Curves on Varieties....Pages 90-158
The Cone Theorem and Minimal Models....Pages 159-178
Rationally Connected Varieties....Pages 179-237
Fano Varieties....Pages 238-284
Appendix....Pages 285-307
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.
Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-4
Hilbert Schemes and Chow Varieties....Pages 5-89
Curves on Varieties....Pages 90-158
The Cone Theorem and Minimal Models....Pages 159-178
Rationally Connected Varieties....Pages 179-237
Fano Varieties....Pages 238-284
Appendix....Pages 285-307
Back Matter....Pages 308-321
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