K-stability of Fano Varieties

Auteur
Chenyang Xu is Professor at Princeton University. He is a fellow of the American Mathematical Society. His contributions have been recognized by the Future Science Prize 2017, the New Horizon Prize 2019, and the Cole Prize 2021.

Texte du rabat

Aimed at graduate students and researchers in algebraic geometry, this is the first book to give a comprehensive and self-contained algebraic treatment of the emerging field of K-stability. It introduces all the notions of K-stability used over the development of the subject, proves their equivalence, and discusses newly developed theory.

Contenu

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.