The Calabi Problem for Fano Threefolds

ISBN-13: 9781009193399 / Angielski

Carolina Araujo; Ana-Maria Castravet; Ivan Cheltsov

Opis

This book determines whether the general member of each family of smooth Fano threefolds admits a Kahler-Einstein metric, using K-stability. Complemented by appendices outlining results needed to understand this active area, it will be essential reading for researchers and graduate students working on algebraic and complex geometry.

Recenzje

'It is a difficult problem to check whether a given Fano variety is K-polystable. This book settles this problem for the general members of all the 105 deformation families of smooth Fano 3-folds. The book is recommended to anyone interested in K-stability and existence of Kähler-Einstein metrics on Fano varieties.' Caucher Birkar FRS, Tsinghua University and University of Cambridge

Spis treści

Introduction; 1. K-stability; 2. Warm-up: smooth del Pezzo surfaces; 3. Proof of main theorem: known cases; 4. Proof of main theorem: special cases; 5. Proof of main theorem: remaining cases; 6. The big table; 7. Conclusion; Appendix. Technical results used in proof of main theorem; References; Index.