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OverviewThe 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. Full Product DetailsAuthor: Toshiki MabuchiPublisher: Springer Verlag, Singapore Imprint: Springer Verlag, Singapore Edition: 1st ed. 2021 Weight: 0.454kg ISBN: 9789811604997ISBN 10: 9811604991 Pages: 128 Publication Date: 26 March 2021 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsIntroduction.- 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.Reviews“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) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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