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Full Description
The K-stability of Fano varieties has been a major area of research over the last decade, ever since the Yau-Tian-Donaldson conjecture was resolved. This is the first book to give a comprehensive algebraic treatment of this emerging field. It introduces all the notions of K-stability that have been used over the development of the subject, proves their equivalence, and discusses newly developed theory, including several new proofs for existing theorems. Aiming to be as self-contained as possible, the text begins with a chapter covering essential background knowledge, and includes exercises throughout to test understanding. Written by an author at the forefront of developments in the area, it will be a source of inspiration for graduate students and researchers who work in algebraic geometry.
Contents
Preface; Notion and conventions; Preliminaries; 1. Higher dimensional geometry background; 2. K-stability via test configurations; 3. K-stability via filtrations; 4. K-stability via valuations; 5. Higher rank finite generation; 6. Reduced stability; 7. K-moduli stack; 8. K-moduli space; 9. Positivity of the CM line bundle; Appendix A. Solutions to exercises; Bibliography; Glossary; Index.
