各类紧致复流形的变形开性和闭性;实例

大基本群的形变开性及其应用

Deformation Openness of Big Fundamental Groups and Applications

本文证明了具有大复局部系统的光滑射影簇的大基本群性质在小形变下稳定，还研究了更一般的Γ-维数形变不变猜想，并发展相关技术得到伪Brody双曲性形变开性等应用。

Seshadri's criterion and openness of projectivity

We prove that projectivity is an open condition for deformations of algebraic spaces with rational singularities. V.2: references updated and corrected.

紧致凯勒双曲流形的全纯形变

Holomorphic Deformations of Compact Kähler Hyperbolic Manifolds

本文研究紧致凯勒双曲流形的形变问题，通过提出凯勒双曲性的修正版本，为探讨 Gromov 经典凯勒双曲性的形变开性迈出第一步。

Deformation Stability of p-SKT and p-HS manifolds

In this paper, we introduce the notions of $p$-Hermitian-symplectic and $p$-pluriclosed compact complex manifolds as generalisations for an arbitrary positive integer $p$ not exceeding the complex dimension of the manifold of the standard notions of Hermitian-symplectic and SKT manifolds that correspond to the case $p=1$. We then notice that these two properties are equivalent on $\partial\bar{\partial}$-manifolds and go on to prove that in (smooth) complex analytic families of $\partial\bar{\partial}$-manifolds, they are deformation open. Concerning closedness results, we prove that the cones…

Geometry of logarithmic forms and deformations of complex structures

We present a new method to solve certain $\bar{\partial}$-equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The result can be considered as a $\bar{\partial}$-lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness of logarithmic forms, give geometric and simpler proofs of Deligne's degeneracy theorem for the logarithmic Hodge to de Rham spectral sequences at $E_1$-level, as well as certain injectivity theorem on compact Kahler manifolds. Furthermore, for a family of logarithmic deformatio…

与光滑除子相关的紧致凯勒流形上的对数$\bar{\partial}$-方程

A logarithmic $\bar{\partial}$-equation on a compact Kähler manifold associated to a smooth divisor

本研究利用循环覆盖技巧求解紧致凯勒流形上与光滑除子相关的对数$\bar{\partial}$-方程，探讨对数形式闭性、单射性定理及谱序列退化，并证明相关对的形变无障碍。