Test configurations, stabilities and canonical Kähler metrics : complex geometry by the energy method
著者
書誌事項
Test configurations, stabilities and canonical Kähler metrics : complex geometry by the energy method
（SpringerBriefs in mathematics）
Springer, c2021
- : pbk
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注記
Includes bibliographical references (p. 125-128)
内容説明・目次
内容説明
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 Kahler 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 Kahler metrics.
目次
Introduction.- The Donaldson-Futaki invariant.- Canonical Kahler metrics.- Norms for test configurations.- Stabilities for polarized algebraic manifolds.- The Yau-Tian-Donaldson conjecture.- Stability theorem.- Existence problem.- Canonical Kahler metrics on Fano manifolds.- Geometry of pseudo-normed graded algebras.- Solutions.
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