My PhD Thesis Project: Kähler minimal model program

The aim of these notes is to introduce the minimal model program for Kähler varieties.

Part I. My PhD Thesis on Kähler minimal model program

My PhD Dissertation Defense Slides: The Kähler Minimal Model Program and Its Applications to Deformation Problems

My PhD Thesis: The Kähler Minimal Model Program and Its Applications to Deformation Problems (in preparation)

My PhD Thesis (Chinese version): 凯勒极小模型纲领及其在变形理论中的应用 (in preparation)

Part II. Reading Notes on the Kähler minimal model program

Note-0 An Overview of the Kähler Minimal Model Program [Video] [upd 9.13]

Note-1 Quasi-psh Functions, currents, and Lelong Numbers [TODO]

Note-2 Positivities and Cones in the Kähler MMP [upd 10.10]

Note-3 Transcendental Volume Function

Note-4 Boucksom’s Divisorial Zariski Decomposition [TODO]

Note-5 Generalized Kähler Pairs [TODO]

Note-6 Existence of MMP for projective morphism between analytic varieties (in preparation)

Note-7 Rational Curves on Compact Kähler Manifolds [upd 5.23]

Note-8 Cone Theorem for the Kähler MMP [upd 12.28]

Note-9 Analytic Contraction Theorems [upd 9.28]

Note-10 Projectivity and Kählerness Criteria [upd 9.24]

Note-11 Transcendental Base Point Free Conjecture [TODO]

Note-12 Existence of MMP in the Kähler Setting [TODO]

Note-13 Finite Generation Problem in the Kähler Setting [TODO]

Note-14 Canonical Bundle Formulas and Subadjunction with Applications in the Kähler MMP (in preparation)

Note-15 Abundance for Kähler Threefolds (in preparation)

Note-16 Applications of the Kähler MMP (in preparation)

Note-17 On the Kähler 3-Fold and 4-Fold MMP [TODO]

Supplement: Tools That Can Be Used to Reduce a Kähler Problem to a Projective Problem