Homogeneous CR-solvmanifolds as Kahler obstructions

On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures

The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact $4$-dimensional solvmanifolds without any integrable almost complex structure. According to the classification theory we consider: $\mathfrak{r}\mathfrak{r}_{3, -1}$, $\mathfrak{nil}^4$ and $\mathfrak{r}_{4, λ, -(1 + λ)}$ with $-1 < λ< -\frac{1}{2}$. For the first solvmanifold we introduce special families of almost complex structures, compute the corresponding Kodaira dimension and show that it is no longer a deformation invariant. Moreover we prove Ricci flatness …

Remarks on astheno-Kahler manifolds, Bott-Chern and Aeppli cohomology groups

We provide a new cohomological obstruction to the existence of astheno-Kahler metrics, and study relevant examples.

广义近凯勒-里奇孤立子

Generalized almost-Kähler-Ricci solitons

本文将凯勒-里奇孤立子推广至近凯勒情形，证明其存在阻碍第一陈-爱因斯坦度量，并给出四维形变结果及松岛定理的部分推广。

关于紧致凯勒流形上解析子集邻域上全纯线丛的形式原理

Formal principle for line bundles on neighborhoods of an analytic subset of a compact Kähler manifold

本文研究了紧致凯勒流形上解析子集邻域全纯线丛的形式原理，通过上同调准则和构造反例揭示了形式原理在族中的不稳定性。

SKT与平衡度量的变分方法

A Variational Approach to SKT and Balanced Metrics

本文针对SKT与平衡度量定义新泛函，证明其临界点恰为Kähler度量，为Kähler性障碍研究提供新途径。

关于格劳尔特例子上一个非半正的 nef 和大线丛

On the Non-Semipositivity of a Nef and Big Line Bundle on Grauert's Example

本研究通过计算格劳尔特例子上的第一障碍类，证明了该线丛是 nef 且大但不半正。