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Kähler metrics on projective manifolds
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Classroom Contents
Canonical Kaehler Metrics and Stability of Algebraic Varieties
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- 1 Intro
- 2 Table of Contents
- 3 Kähler manifolds and Kähler metrics
- 4 Kähler metrics on projective manifolds
- 5 Holomorphic sectional curvature
- 6 Ricci Curvature and scalar curvature
- 7 Constant scalar curvature Kähler (csc) metrics
- 8 (Uniform) Yau-Tian-Donaldson (YTD) conjecture
- 9 A recent progress: a model version of YTD
- 10 Kähler-Einstein case: G(X) = A(L)
- 11 Space of Kähler metrics Space of smooth Kahler potentials
- 12 Energy functionals
- 13 Pluripotential theory on compact Kähler manifolds
- 14 Variational point of view
- 15 Variational criterion
- 16 Criterion via geodesic rays
- 17 Test configurations (Tian, Donaldson) A test configuration (TC) (X.C:n) for (X. 2) is the following data
- 18 Algebraic functionals of TCS (with reduced fibre)
- 19 Uniform K-stability We use a strengthened version of K stability Tian, Donaldson
- 20 K-stability of Fano varieties
- 21 Fano case: special test configurations
- 22 Fano case: flourishing strong/deep results
- 23 Analytic vs. algebraic invariants of (x,c)
- 24 Approximation approach to (uniform) YTD conjecture
- 25 Destabilizing geodesic rays are algebraically approximab
- 26 K-stability over models
- 27 Approximation by models
- 28 An algebro-geometric conjecture
