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Test Configurations, Stabilities and Canonical Kähler Metrics

Test Configurations, Stabilities and Canonical Kähler Metrics Complex Geometry by the Energy Method - SpringerBriefs in Mathematics

1st Edition 2021

Paperback (26 Mar 2021)

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Publisher's Synopsis

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.

Book information

ISBN: 9789811604997
Publisher: Springer Nature Singapore
Imprint: Springer
Pub date:
Edition: 1st Edition 2021
Language: English
Number of pages: 128
Weight: 238g
Height: 233mm
Width: 155mm
Spine width: 12mm