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＜電子ブック＞
Test Configurations, Stabilities and Canonical Kähler Metrics : Complex Geometry by the Energy Method / by Toshiki Mabuchi
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2021.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2021
大きさ	X, 128 p. 37 illus : online resource
著者標目	*Mabuchi, Toshiki author SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Functions of complex variables LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Algebraic geometry FREE:Differential Geometry FREE:Several Complex Variables and Analytic Spaces FREE:Global Analysis and Analysis on Manifolds FREE:Algebraic Geometry
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-981-16-0500-0

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