Front Matter
 Introduction
 Chapter 1. Preliminary Material Cohomology, Currents
  1.A. Dolbeault Cohomology and Sheaf Cohomology
  1.B. Plurisubharmonic Functions
  1.C. Positive Currents
 Chapter 2. Lelong numbers and Intersection Theory
  2.A. Multiplication of Currents and Monge-Amp_ere Operators
  2.B. Lelong Numbers
 Chapter 3. Hermitian Vector Bundles, Connections and Curvature
 Chapter 4. Bochner Technique and Vanishing Theorems
  4.A. Laplace-Beltrami Operators and Hodge Theory
  4.B. Serre Duality Theorem
  chner-Kodaira-Nakano Identity on Kahler Manifolds
  4.D. Vanishing Theorems
 Chapter 5. L2 Estimates and Existence Theorems
  5.A. Basic L2 Existence Theorems
  5.B. Multiplier Ideal Sheaves and Nadel Vanishing Theorem
 Chapter 6. Numerically E_ective andPseudo-e_ective Line Bundles
  6.A. Pseudo-e_ective Line Bundles and Metrics with Minimal Singularities
  6.B. Nef Line Bundles
  6.C. Description of the Positive Cones
  6.D. The Kawamata-Viehweg Vanishing Theorem
  6.E. A Uniform Global Generation Property due to Y.T. Siu
 Chapter 7. A Simple Algebraic Approach to Fujita’s Conjecture
 Chapter 8. Holomorphic Morse Inequalities
  8.A. General Analytic Statement on Compact Complex Manifolds
  8.B. Algebraic Counterparts of the Holomorphic Morse Inequalities
  8.C. Asymptotic Cohomology Groups
  8.D. Transcendental Asymptotic Cohomology Functions
 Chapter 9. E_ective Version of Matsusaka’s Big Theorem
 Chapter 10. Positivity Concepts for Vector Bundles
 Chapter 11. Skoda’s L2 Estimates for Surjective Bundle Morphisms
  11.A. Surjectivity and Division Theorems
  11.B. Applications to Local Algebra the Brian_con-Skoda Theorem
  8 Analytic Methods in Algebraic Geometry
 Chapter 12. The Ohsawa-Takegoshi L2 Extension Theorem
  12.A. The Basic a Priori Inequality
  12.B. Abstract L2 Existence Theorem for Solutions of @-Equations
  12.C. The L2 Extension Theorem
  12.D. Skoda’s Division Theorem for Ideals of Holomorphic Functions
 Chapter 13. Approximation of Closed Positive Currents by Analytic Cycles
  13.A. Approximation of Plurisubharmonic Functions Via Bergman Kernels
  13.B. Global Approximation of Closed (1,1)-currents on a Compact Complex Manifold
  13.C. Global Approximation by Divisors
  13.D. Singularity Exponents and log Canonical Thresholds
  13.E. Hodge Conjecture and approximation of (p; p)- currents
 Chapter 14. Subadditivity of Multiplier Ideals and Fujita’s Approximate Zariski Decomposition
 Chapter 15. Hard Lefschetz Theorem with Multiplier Ideal Sheaves
  15.A. A Bundle Valued Hard Lefschetz Theorem
  15.B. Equisingular Approximations of Quasi Plurisubharmonic Functions
  15.C. A Bochner Type Inequality
  15.D. Proof of Theorem 15.1
  15.E. A Counterexample
 Chapter 16. Invariance of Plurigenera of Projective Varieties
 Chapter 17. Numerical Characterization of the Kahler Cone
  17.A. Positive Classes in Intermediate (p; p)-bidegrees
  17.B. Numerically Positive Classes of Type (1,1)
  17.C. Deformations of Compact Kahler Manifolds
 Chapter 18. Structure of the Pseudo-e_ective Cone and Mobile Intersection Theory
  18.A. Classes of Mobile Curves and of Mobile (n -1; n-1)-currents
  18.B. Zariski Decomposition and Mobile Intersections
  18.C. The Orthogonality Estimate
  18.D. Dual of the Pseudo-e_ective Cone
  18.E. A Volume Formula for Algebraic (1,1)-classes on Projective Surfaces
 Chapter 19. Super-canonical Metrics and Abundance
  19.A. Construction of Super-canonical Metrics
  19.B. Invariance of Plurigenera and Positivity of Curvature of Super-canonical Metrics
  19.C. Tsuji’s Strategy for Studying Abundance
 Chapter 20. Siu’s Analytic Approach and P_aun’s Non Vanishing Theorem
 References
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