04649nam 2200589 450 99646655000331620220610120827.0981-16-0500-9(CKB)4100000011807312(MiAaPQ)EBC6527495(Au-PeEL)EBL6527495(OCoLC)1243514520(PPN)254721346(EXLCZ)99410000001180731220211015d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierTest configurations, stabilities and canonical Kähler metrics complex geometry by the energy method /Toshiki MabuchiSingapore :Springer,[2021]©20211 online resource (x, 128 pages) illustrationsSpringerBriefs in Mathematics981-16-0499-1 Includes bibliographical references.Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Preliminaries -- 1.2 The Deligne Pairings with Metrics -- 1.3 Definition of the Chow Norm -- 1.4 The First and Second Variation Formulas for the Chow Norm -- Problems -- 2 The Donaldson-Futaki Invariant -- 2.1 Test Configurations -- 2.2 Test Configurations Associated to One-Parameter Groups -- 2.3 Definition of the Donaldson-Futaki Invariant -- 2.4 Expression of DF1 as an Intersection Number -- 2.5 The Relationship Between the Chow Norm and DFi -- Problems -- 3 Canonical Kähler Metrics -- 3.1 Canonical Kähler Metrics on Compact Complex Manifolds -- 3.2 Conformal Changes of Metrics by Hamiltonian Functions -- Problems -- 4 Norms for Test Configurations -- 4.1 Norms for Test Configurations of a Fixed Exponent -- 4.2 The Asymptotic 1-norm of a Test Configuration -- 4.3 Relative Norms for Test Configurations -- 4.4 The Twisted Kodaira Embedding -- 4.5 The Donaldson-Futaki Invariant for Sequences -- Problems -- 5 Stabilities for Polarized Algebraic Manifolds -- 5.1 The Chow Stability -- 5.2 The Hilbert Stability -- 5.3 K-stability -- 5.4 Relative Stability -- Problems -- 6 The Yau-Tian-Donaldson Conjecture -- 6.1 The Calabi Conjecture -- 6.2 The Yau-Tian-Donaldson Conjecture -- 6.3 The K-Energy -- 6.4 Extremal Kähler Versions of the Conjecture -- Problems -- 7 Stability Theorem -- 7.1 Strong K-Semistability of CSC Kähler Manifolds -- 7.2 Relative Balanced Metrics -- 7.3 Strong Relative K-Semistability of Extremal Kähler Manifolds -- 7.4 K-Polystability of Extremal Kähler Manifolds -- 7.5 A Reformulation of the Definition of the Invariant F ({μj}) -- Problems -- 8 Existence Problem -- 8.1 A Result of He on the Existence of Extremal Kähler Metrics -- 8.2 Some Observations on the Existence Problem -- Problems -- 9 Canonical Kähler Metrics on Fano Manifolds -- 9.1 Kähler Metrics in Anticanonical Class.9.2 Extremal Vector Fields -- 9.3 An Obstruction of Matsushima's Type -- 9.4 An Invariant as an Obstruction to the Existence -- 9.5 Examples of Generalized Kähler-Einstein Metrics -- 9.6 Extremal Metrics on Generalized Kähler-Einstein Manifolds -- 9.7 The Product Formula for the Invariant γX -- 9.8 Yao's Result for Toric Fano Manifolds -- 9.9 Hisamoto's Result on the Existence Problem -- Problems -- A Geometry of Pseudo-Normed Graded Algebras -- A.1 Differential Geometric Viewpoints -- A.2 Lp-Spaces -- A.3 An Orthogonal Direct Sum of Lp-Spaces -- A.4 A Boundedness Theorem for Lp-Spaces -- A.5 The Moduli Space of Lp-Spaces -- A.6 A Multiplicative System of Lp-Spaces -- A.7 Degeneration Phenomena -- Solutions -- Problems of Chap.1 -- Problems of Chap.2 -- Problems of Chap.3 -- Problems of Chap.4 -- Problems of Chap.5 -- Problems of Chap.6 -- Problems of Chap.7 -- Problems of Chap.8 -- Problems of Chap.9 -- Bibliography.SpringerBriefs in mathematics.Geometry, DifferentialManifolds (Mathematics)Moduli theoryGeometria diferencialthubVarietats (Matemàtica)thubTeoria de mòdulsthubLlibres electrònicsthubGeometry, Differential.Manifolds (Mathematics)Moduli theory.Geometria diferencialVarietats (Matemàtica)Teoria de mòduls516.36Mabuchi Toshiki1950-60370MiAaPQMiAaPQMiAaPQBOOK996466550003316Test configurations, stabilities and canonical Kähler metrics1904802UNISA01694nas 2200553-- 450 991033902550332120240915213022.0(CKB)958480250571(CONSER)---77617242-(EXLCZ)9995848025057120750716b1970198u --- aengtxtrdacontentcrdamediacrrdacarrierSystems, computers, controls[Washington]Scripta Pub Co1 online resourceRefereed/Peer-reviewedPrint version: Systems, computers, controls. 0096-8765 (DLC) 77617242 (OCoLC)1453340 Scripta electronica Japonica IIISyst. comput. controlsSystem analysisPeriodicalsElectronic digital computersPeriodicalsAutomatic controlPeriodicalsAutomatic controlfastElectronic digital computersfastSystem analysisfastDatenverarbeitunggndZeitschriftgndJapangndPeriodicalsfastPeriodicals.lcgftSystem analysisElectronic digital computersAutomatic controlAutomatic controlElectronic digital computersSystem analysisDatenverarbeitung.Zeitschrift.003/.05621Scripta Technica, inc.JOURNAL9910339025503321exl_impl conversionSystems, computers, controls2171726UNINA