The Calabi Problem for Fano Threefolds (Paperback)

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.

General

Imprint:	Cambridge UniversityPress
Country of origin:	United Kingdom
Series:	London Mathematical Society Lecture Note Series
Release date:	June 2023
Authors:	Carolina Araujo • Ana-Maria Castravet • Ivan Cheltsov • Kento Fujita • Anne-Sophie Kaloghiros • Jesus Martinez-Garcia • Constantin Shramov • Hendrik Süß • Nivedita Viswanathan
Dimensions:	229 x 152 x 25mm (L x W x T)
Format:	Paperback
Pages:	455
ISBN-13:	978-1-00-919339-9
Categories:	Books
LSN:	1-00-919339-2
Barcode:	9781009193399

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