# Reference for the Hodge diamond of the Iwasawa threefold

Let $$X = G/\Gamma$$ denote the Iwasawa threefold, where

$$G = \left\{\begin{pmatrix} 1 & z_1 & z_3\\ 0 & 1 & z_2\\ 0 & 0 & 1\end{pmatrix} : z_1, z_2, z_3 \in \mathbb{C} \right\},$$

and $$\Gamma$$ is the discrete subgroup $$\Gamma=\left\{\begin{pmatrix} 1 & z_1 & z_3\\ 0 & 1 & z_2\\ 0 & 0 & 1\end{pmatrix} : z_1, z_2, z_3 \in \mathbb{Z}[i] \right\}.$$

Can anyone point to a reference for the Hodge diamond of $$X$$?

## 1 Answer

Should have waited a few minutes, it's on page 49 of Danielle Angela's Cohomological aspects of non-Kähler manifolds: https://arxiv.org/pdf/1302.0524.pdf