Test Configurations, Stabilities and Canonical Kähler Metrics

Download or read book Test Configurations, Stabilities and Canonical Kähler Metrics written by Toshiki Mabuchi and published by Springer Nature. This book was released on 2021-03-25 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.