K-stability of Fano Varieties

Chenyang Xu (Princeton University, New Jersey)

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English

Cambridge University Press
30 April 2025

Differential & Riemannian geometry; Algebraic geometry

Series: New Mathematical Monographs

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.

By: Chenyang Xu (Princeton University New Jersey)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
ISBN: 9781009538770
ISBN 10: 1009538772
Series: New Mathematical Monographs
Pages: 415
Publication Date: 30 April 2025
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Forthcoming

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.