The Calabi Problem for Fano Threefolds

di Carolina Araujo (Autore)

Ana-Maria Castravet (Autore)

Ivan Cheltsov (Autore)

Cambridge University Press, 2023

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.

• Autore: Carolina Araujo, Ana-Maria Castravet, Ivan Cheltsov
• Editore: Cambridge University Press
• Collana: London Mathematical Society Lecture Note Series
• Anno: 2023
• Rilegatura: Paperback / softback
• Pagine: 455 p.
• Dimensioni: 229 x 152 mm
• Peso: 680 gr.
• EAN: 9781009193399

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