Study of moduli spaces of projective varieties of general type

我得到了一个仅依赖于n的正数m(n)，使得对于每一个一般类型的光滑射影n折和每一个正整数m> m(n)， mK_{X}给出了X在射影空间中的一个二元嵌入。这是E. Bombieri对一般型曲面结果的进一步推广。其次，证明了对于光滑射影族X长直线S和半正奇异厄米线束L，其伴随束K {X/S} + L在X上具有对数次调和的Bergman核。此外，曲率电流作为闭合正电流延伸到整个完井。第三，我证明了具有负里奇曲率的Kaehler-Einstein度规的新构造。这使我们能够研究Kaehler-Einstein体积形式在正则极化的光滑射影族上的变化。因此，我得到了光滑射影族上Kaehler-Einstein体积形式的多次谐波变分。我在具有半正曲率电流的任意非正则射影变的正则束上构造了一个正则奇异厄米度规。最小奇点（AZD）。这使我们能够得到一个非常简短的证明，证明多属的不变性。

I obtain that there exists a positive number m(n) dependeing only on n such that for every smooth projective n-fold of general type and for every positive integer m> m(n), mK_{X} gives a birtaional embedding of X into a projective space.This is a furthere generalization of the result of E. Bombieri for surfaces of general type.Next I proved that the for a smooth projective family f X longrightarrow S and a semipositive singular hermitian line bundle L,The adjoint bundle K {X/S} + L has a Bergman kernel which is logarithmically plurisubharmonic on $X$.Moreover the curvature current extends to the whole completion as a closed positive current.3rd I have proven a new construction of Kaehler-Einstein metric with negative Ricci curvature. This enables us to study the variation of Kaehler-Einstein volume form on a smooth projective family of canonically polarized varieties.As a consequence I have obtained the plurisubharmonic variation of the Kaehler-Einstein volume form on a smooth projective Family.4^<th>. I have constructed a canonical singular hermitian metric on the canonical bundle of any nonuniruled projective varieties with semipositive curvature current. And minimal singularities (AZD).This enables us to obtain a very short proof of the invariance of plurigenera.