Test Configurations, Stabilities and Canonical Kähler Metrics
Complex Geometry by the Energy Method
Published on 25. March 2021
X, 128 pages
978-981-16-0500-0 (ISBN)
Description
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.Reviews / Votes
"The concise style of exposition likely means that this monograph is best suited for experts with background knowledge in canonical Kähler metrics. . It can be recommended also to those who would like a review of important results concerning the generalised Kähler-Einstein metrics, with various examples, and the moduli space of Lp-spaces." (Yoshinori Hashimoto, Mathematical Reviews, May, 2023)More details
Series
Edition
1st ed. 2021
Language
English
Place of publication
Singapore
Singapore
Publishing group
Springer Singapore
Target group
Primary & secondary/elementary & high school
Product notice
Reflowable
Illustrations
X, 128 p. 37 illus.
File size
2,65 MB
ISBN-13
978-981-16-0500-0 (9789811605000)
DOI
10.1007/978-981-16-0500-0
Schweitzer Classification
Other editions
Additional editions
Toshiki Mabuchi
Test Configurations, Stabilities and Canonical Kähler Metrics
Complex Geometry by the Energy Method
Book
03/2021
Springer
€69.54
Shipment within 3-4 weeks
Content
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.
