The Calabi Problem for Fano Threefolds
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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 K hler-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 K hler-Einstein metric, containing many additional relevant results such as the classification of all K hler-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.
Format:Paperback
Language:English
ISBN:1009193392
ISBN13:9781009193399
Release Date:June 2023
Publisher:Cambridge University Press
Length:455 Pages
Weight:1.45 lbs.
Dimensions:1.0" x 5.9" x 8.9"
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