Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This book determines whether the general element of each family admits a Kähler-Einstein metric (and for many families, for all elements), addressing a question going back to Calabi 70 years ago. The book's solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, the book presents many different techniques to prove the existence of a Kähler-Einstein metric, containing many additional relevant results such as the classification of all Kähler-Einstein smooth Fano threefolds with infinite automorphism groups and computations of delta-invariants of all smooth del Pezzo surfaces. This book will be essential reading for researchers and graduate students working on algebraic geometry and complex geometry.

Author: Carolina Araujo, Ana-Maria Castravet, Ivan Cheltsov
Binding Type: Paperback
Publisher: Cambridge University Press
Published: 06/29/2023
Series: London Mathematical Society Lecture Note #485
Pages: 455
Weight: 1.45lbs
Size: 8.90h x 5.91w x 1.02d
ISBN: 9781009193399