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The Calabi Problem for Fano Threefolds

By Carolina Araujo

The Calabi Problem for Fano Threefolds

By Carolina Araujo

- Default Title
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 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.
Product details
Binding:
Paperback
Edition:
1
Number of Pages:
450
Release Date:
2023-06-29
Publication Date:
2023-06-29
Publisher:
Cambridge University Press
Languages:
Original: English
ISBN10:
1009193392
ISBN13:
9781009193399
GPSR Manufacturer Reference:
[email protected]
Weight:
647 g
Height:
152 cm
Width:
229 cm
Thickness:
24 cm
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