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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
The Calabi Problem for Fano Threefolds

The Calabi Problem for Fano Threefolds

Araujo, Carolina
Castravet, Ana-Maria
Cheltsov, Ivan

Paperback

Series: London Mathematical Society Lecture Note, Book 485

General Mathematics

ISBN10: 1009193392
ISBN13: 9781009193399
Publisher: Cambridge University Press
Published: Jun 29 2023
Pages: 455
Weight: 1.45
Height: 1.02 Width: 5.91 Depth: 8.90
Language: English
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.

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