Test configurations, stabilities and canonical Kähler metrics : complex geometry by the energy method / Toshiki Mabuchi.
2021
QA641
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Title
Test configurations, stabilities and canonical Kähler metrics : complex geometry by the energy method / Toshiki Mabuchi.
ISBN
9789811605000 (electronic bk.)
9811605009 (electronic bk.)
9789811605017 (print)
9811605017
9811604991
9789811604997
9811605009 (electronic bk.)
9789811605017 (print)
9811605017
9811604991
9789811604997
Published
Singapore : Springer, [2021]
Language
English
Description
1 online resource (x, 128 pages) : illustrations
Other Standard Identifiers
10.1007/978-981-16-0500-0 doi
Call Number
QA641
Dewey Decimal Classification
516.3/73
Summary
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.
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Includes bibliographical references.
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text file
PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed April 19, 2021).
Series
SpringerBriefs in mathematics.
Available in Other Form
Print version: 9789811604997
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Table of Contents
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 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.