Test Configurations, Stabilities and Canonical Kähler Metrics: Complex Geometry by the Energy Method

ISBN-13: 9789811604997 / Angielski / Miękka / 2021 / 128 str.

Toshiki Mabuchi

Recenzje

"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)

Spis treści

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.