K-stability of Fano Varieties

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 one of the first books 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.