### Complex-symmetric spaces

A compact complex space $X$ is called complex-symmetric with respect to a subgroup $G$ of the group ${\mathrm{Aut}}_{0}\left(X\right)$, if each point of $X$ is isolated fixed point of an involutive automorphism of $G$. It follows that $G$ is almost ${G}^{0}$-homogeneous. After some examples we classify normal complex-symmetric varieties with ${G}^{0}$ reductive. It turns out that $X$ is a product of a Hermitian symmetric space and a compact torus embedding satisfying some additional conditions. In the smooth case these torus embeddings are classified using...