Del 485 i serien London Mathematical Society Lecture Note Series

The Calabi Problem for Fano Threefolds

Häftad, Engelska, 2023

AvCarolina Araujo,Ana-Maria Castravet,Ivan Cheltsov,Kento Fujita,Anne-Sophie Kaloghiros,Jesus Martinez-Garcia,Constantin Shramov,Hendrik Süß,Nivedita Viswanathan

1 349 kr

Beställningsvara. Skickas inom 7-10 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

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.

Produktinformation

Utgivningsdatum2023-06-29
Mått152 x 229 x 25 mm
Vikt680 g
FormatHäftad
SpråkEngelska
SerieLondon Mathematical Society Lecture Note Series
Antal sidor455
FörlagCambridge University Press
ISBN9781009193399

Tillhör följande kategorier

Algebra inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Carolina Araujo is a researcher at the Institute for Pure and Applied Mathematics (IMPA), Rio de Janeiro, Brazil. Ana-Maria Castravet is Professor at the University of Versailles, France. Ivan Cheltsov is Chair of Birational Geometry at the University of Edinburgh. Kento Fujita is Associate Professor at Osaka University. Anne-Sophie Kaloghiros is a Reader at Brunel University London. Jesus Martinez-Garcia is Senior Lecturer in Pure Mathematics at the University of Essex. Constantin Shramov is a researcher at the Steklov Mathematical Institute, Moscow. Hendrik Süß is Chair of Algebra at the University of Jena, Germany. Nivedita Viswanathan is a Research Associate at Loughborough University.

'The notion of K-stability for Fano manifold has origins in differential geometry and geometric analysis but is now also of fundamental importance in algebraic geometry, with recent developments in moduli theory. This monograph gives an account of a large body of research results from the last decade, studying in depth the case of Fano threefolds. The wealth of material combines in a most attractive way sophisticated modern theory and the detailed study of examples, with a classical flavour. The authors obtain complete results on the K-stability of generic elements of each of the 105 deformation classes. The concluding chapter contains some fascinating conjectures about the 34 families which may contain both stable and unstable manifolds, which will surely be the scene for much further work. The book will be an essential reference for many years to come.' Sir Simon Donaldson, F.R.S., Imperial College London