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Test Configurations, Stabilities and Canonical Kähler Metrics = Complex Geometry by the Energy Method /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Test Configurations, Stabilities and Canonical Kähler Metrics/ by Toshiki Mabuchi.
Reminder of title:	Complex Geometry by the Energy Method /
Author:	Mabuchi, Toshiki.
Description:	X, 128 p. 37 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Differential geometry. -
Online resource:	https://doi.org/10.1007/978-981-16-0500-0
ISBN:	9789811605000

Test Configurations, Stabilities and Canonical Kähler Metrics = Complex Geometry by the Energy Method /
Mabuchi, Toshiki.

Test Configurations, Stabilities and Canonical Kähler MetricsComplex Geometry by the Energy Method /[electronic resource] :by Toshiki Mabuchi. - 1st ed. 2021. - X, 128 p. 37 illus.online resource. - SpringerBriefs in Mathematics,2191-8201. - SpringerBriefs in Mathematics,.

Introduction -- The Donaldson-Futaki invariant -- Canonical Kähler metrics -- Norms for test configurations -- Stabilities for polarized algebraic manifolds -- The Yau-Tian-Donaldson conjecture -- Stability theorem -- Existence problem -- Canonical Kähler metrics on Fano manifolds -- Geometry of pseudo-normed graded algebras -- Solutions. .

The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. However, this conjecture is still open for general polarizations or more generally in extremal Kähler cases. In this book, the unsolved cases of the conjecture will be discussed. It will be shown that the problem is closely related to the geometry of moduli spaces of test configurations for polarized algebraic manifolds. Another important tool in our approach is the Chow norm introduced by Zhang. This is closely related to Ding’s functional, and plays a crucial role in our differential geometric study of stability. By discussing the Chow norm from various points of view, we shall make a systematic study of the existence problem of extremal Kähler metrics.

ISBN: 9789811605000

Standard No.: 10.1007/978-981-16-0500-0doiSubjects--Topical Terms:

882213
Differential geometry.

LC Class. No.: QA641-670

Dewey Class. No.: 516.36

Test Configurations, Stabilities and Canonical Kähler Metrics = Complex Geometry by the Energy Method /
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