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The Calabi problem for Fano threefolds

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Calabi problem for Fano threefoldsCarolina Araujo ... [et al.].
other author:	Araujo, Carolina.
Published:	Cambridge :Cambridge University Press,2023.
Description:	vii, 441 p. :ill., digital ;23 cm.
Notes:	Also issued in print: 2023.
Subject:	Threefolds (Algebraic geometry)
Online resource:	https://doi.org/10.1017/9781009193382
ISBN:	9781009193382

The Calabi problem for Fano threefolds
The Calabi problem for Fano threefolds[electronic resource] /Carolina Araujo ... [et al.]. - Cambridge :Cambridge University Press,2023. - vii, 441 p. :ill., digital ;23 cm. - London Mathematical Society lecture note series ;485. - London Mathematical Society lecture note series ;353..

Also issued in print: 2023.

Includes bibliographical references and index.

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. Its solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, it 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.

Specialized.

ISBN: 9781009193382

Standard No.: 10.1017/9781009193382doiSubjects--Topical Terms:

273067
Threefolds (Algebraic geometry)

LC Class. No.: QA564 / .A7 2023

Dewey Class. No.: 516.353

The Calabi problem for Fano threefolds
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245 0 4 $a The Calabi problem for Fano threefolds $h [electronic resource] / $c Carolina Araujo ... [et al.].
260 $a Cambridge : $b Cambridge University Press, $c 2023.
300 $a vii, 441 p. : $b ill., digital ; $c 23 cm.
490 1 $a London Mathematical Society lecture note series ; $v 485
500 $a Also issued in print: 2023.
504 $a Includes bibliographical references and index.
520 8 $a 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. Its solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, it 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.
521 $a Specialized.
588 $a Description based on online resource; title from PDF title page (viewed on July 4, 2023).
650 0 $a Threefolds (Algebraic geometry) $3 273067
700 1 $a Araujo, Carolina. $3 227600
830 0 $a London Mathematical Society lecture note series ; $v 353. $3 609716
856 4 0 $u https://doi.org/10.1017/9781009193382