界全数VMRT理论在性题上的-HKU.PDF

20 VMRT , , nmok@hkucc.hku.hk Ω X = Ω/Γ ( Γ ⊂ Aut(Ω) ) Calabi-Vesentini[1] Borel[2] . , dimC (X ) 2 , H 1 (X, TX ) = 0, X . [3] , K¨ahler , n 2 K¨ahler N Nakano (strictly positive in the dual-Nakano sense) , N K¨ahler M N . Ω 1 , Ω n 2 . Ω 2 , Nakano , Siu[3,4] X = Ω/Γ . Margulis , 2 (Z, g) , Γ ⊂ Aut(Z, g) . Hermite , , 2 (holomorphic bisectional curvature) . Γ X . [5] X Hermite , X K¨ahler K¨ahler-Einstein . ( ). , X K¨ahler-Einstein . Hermite K¨ahler-Einstein , Mok[5] X = Ω/Γ Hermite , [6] Satake-Baily-Borel . 2 Ω . (N, h) K¨ahler . Hermite , , X = Ω/Γ K¨ahler (N, h) 20 VMRT · 493 · . , D Aut(D) K¨ahler . , , Finsler . , D Aut(D) Carath´eodory . Hermite Finsler , Ω Γ , Ω D ⊂ Cn Φ : Γ → Aut(D) . , Finsler . , Finsler () . , Γ . X = Ω/Γ Ω