Kaehler流形的射影性- Kodaira问题（在C. Voisin）

Projectivity of the moduli space of stable log-varieties and subadditvity of log-Kodaira dimension

We prove a strengthening of Kollár's Ampleness Lemma and use it to prove that any proper coarse moduli space of stable log-varieties of general type is projective. We also prove subadditivity of log-Kodaira dimension for fiber spaces whose general fiber is of log general type.

On the Kodaira problem for uniruled Kähler spaces

We discuss the Kodaira problem for uniruled Kähler spaces. Building on a construction due to Voisin, we give an example of a uniruled Kähler space $X$ such that every run of the $K_X$-MMP immediately terminates with a Mori fibre space, yet $X$ does not admit an algebraic approximation. Our example also shows that for a Mori fibration, approximability of the base does not imply approximability of the total space.

解析Hilbert和Kaehler投影的射影性

Projectivity of analytic Hilbert and Kaehler quotients

本文利用复约化李群G研究了复空间的代数性。得到了代数G-簇的紧动量映射子的射影性结果。此外，我们证明等变版本的Kodaira的嵌入定理和周定理相对于分析希尔伯特商。结合这些结果，我们得到一个等变代数定理的复空间与投射商。

Kähler流形的形变

Deformation of Kähler manifolds

Claire Voisin在2003年证明了一个紧致的Kähler流形不可能总是变形为射影代数流形，从而否定了Kodaira提出的一个问题。本文证明了在典范丛上附加半正性或半负性条件下，答案为正，即这样的紧致Kähler流形可以用射影流形的变形来逼近.