LEADER 04649nam 2200589 450 001 996466550003316 005 20220610120827.0 010 $a981-16-0500-9 035 $a(CKB)4100000011807312 035 $a(MiAaPQ)EBC6527495 035 $a(Au-PeEL)EBL6527495 035 $a(OCoLC)1243514520 035 $a(PPN)254721346 035 $a(EXLCZ)994100000011807312 100 $a20211015d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTest configurations, stabilities and canonical Ka?hler metrics $ecomplex geometry by the energy method /$fToshiki Mabuchi 210 1$aSingapore :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (x, 128 pages) $cillustrations 225 1 $aSpringerBriefs in Mathematics 311 $a981-16-0499-1 320 $aIncludes bibliographical references. 327 $aIntro -- 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 Ka?hler Metrics -- 3.1 Canonical Ka?hler 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 Ka?hler Versions of the Conjecture -- Problems -- 7 Stability Theorem -- 7.1 Strong K-Semistability of CSC Ka?hler Manifolds -- 7.2 Relative Balanced Metrics -- 7.3 Strong Relative K-Semistability of Extremal Ka?hler Manifolds -- 7.4 K-Polystability of Extremal Ka?hler Manifolds -- 7.5 A Reformulation of the Definition of the Invariant F ({?j}) -- Problems -- 8 Existence Problem -- 8.1 A Result of He on the Existence of Extremal Ka?hler Metrics -- 8.2 Some Observations on the Existence Problem -- Problems -- 9 Canonical Ka?hler Metrics on Fano Manifolds -- 9.1 Ka?hler Metrics in Anticanonical Class. 327 $a9.2 Extremal Vector Fields -- 9.3 An Obstruction of Matsushima's Type -- 9.4 An Invariant as an Obstruction to the Existence -- 9.5 Examples of Generalized Ka?hler-Einstein Metrics -- 9.6 Extremal Metrics on Generalized Ka?hler-Einstein Manifolds -- 9.7 The Product Formula for the Invariant ?X -- 9.8 Yao's Result for Toric Fano Manifolds -- 9.9 Hisamoto's Result on the Existence Problem -- Problems -- A Geometry of Pseudo-Normed Graded Algebras -- A.1 Differential Geometric Viewpoints -- A.2 Lp-Spaces -- A.3 An Orthogonal Direct Sum of Lp-Spaces -- A.4 A Boundedness Theorem for Lp-Spaces -- A.5 The Moduli Space of Lp-Spaces -- A.6 A Multiplicative System of Lp-Spaces -- A.7 Degeneration Phenomena -- Solutions -- Problems of Chap.1 -- Problems of Chap.2 -- Problems of Chap.3 -- Problems of Chap.4 -- Problems of Chap.5 -- Problems of Chap.6 -- Problems of Chap.7 -- Problems of Chap.8 -- Problems of Chap.9 -- Bibliography. 410 0$aSpringerBriefs in mathematics. 606 $aGeometry, Differential 606 $aManifolds (Mathematics) 606 $aModuli theory 606 $aGeometria diferencial$2thub 606 $aVarietats (Matemàtica)$2thub 606 $aTeoria de mòduls$2thub 608 $aLlibres electrònics$2thub 615 0$aGeometry, Differential. 615 0$aManifolds (Mathematics) 615 0$aModuli theory. 615 7$aGeometria diferencial 615 7$aVarietats (Matemàtica) 615 7$aTeoria de mòduls 676 $a516.36 700 $aMabuchi$b Toshiki$f1950-$060370 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466550003316 996 $aTest configurations, stabilities and canonical Ka?hler metrics$91904802 997 $aUNISA