论文标题
在几乎复杂的4维溶剂固定物的Kodaira维度上，没有复杂的结构
On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures
论文作者
论文摘要
本文的目的是继续研究Kodaira维度几乎复杂的歧管，重点是紧凑型$ 4 $维的Solvmanifolds，而没有任何可集成的几乎复杂的结构。根据分类理论，我们考虑：$ \ Mathfrak {r} \ Mathfrak {r} _ {3，-1} $，$ \ Mathfrak {nil}^4 $和$ \ Mathfrak {r} _ {r} _ {4，λ，λ， - ， - （1 +λ）} $ with $ -1 <λ<-eλ<--} $} $}对于第一个Solvmanifold，我们介绍了几乎复杂结构的特殊系列，计算相应的Kodaira维度，并表明它不再是变形不变。此外，我们证明了几乎是Kähler结构的规范连接的Ricci平坦度。关于其他两个歧管，我们为某些几乎复杂的结构计算Kodaira维度。最后，我们构建了一个自然的超复合结构，提供了扭曲描述。
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 of the canonical connection for the almost Kähler structure. Regarding the other two manifolds we compute the Kodaira dimension for certain almost complex structures. Finally we construct a natural hypercomplex structure providing a twistorial description.
