The Calabi Problem for Fano Threefolds Paperback / softback
by Carolina (Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro) Araujo, Ana-Maria (Universite Versailles/Saint Quentin-en-Yvelines) Castravet, Ivan (University of Edinburgh) Cheltsov, Kento (Osaka University, Japan) Fujita, Anne-Sophie (Brunel University) Kaloghiros, Jesus (University of Essex) Martinez-Garcia, Constantin (Steklov Mathematical Institute, Moscow) Shramov, Hendrik (Friedrich-Schiller-Universitat, Jena, Germany) Suss, Nivedita (Loughborough University) Viswanathan
Part of the London Mathematical Society Lecture Note Series series
Paperback / softback
Description
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 Kahler-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 Kahler-Einstein metric, containing many additional relevant results such as the classification of all Kahler-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.
Information
-
Only a few left - usually despatched within 24 hours
- Format:Paperback / softback
- Pages:455 pages, Worked examples or Exercises
- Publisher:Cambridge University Press
- Publication Date:29/06/2023
- Category:
- ISBN:9781009193399
Information
-
Only a few left - usually despatched within 24 hours
- Format:Paperback / softback
- Pages:455 pages, Worked examples or Exercises
- Publisher:Cambridge University Press
- Publication Date:29/06/2023
- Category:
- ISBN:9781009193399
