Let $ℐ$ be a coherent subsheaf of a locally free sheaf $𝒪\left(E_0\right)$ and suppose that $ℱ=𝒪\left(E_0\right)/ℐ$ has pure codimension. Starting with a residue current $R$ obtained from a locally free resolution of $ℱ$ we construct a vector-valued Coleff-Herrera current $\mu$ with support on the variety associated to $ℱ$ such that $\phi$ is in $ℐ$ if and only if $\mu \phi =0$. Such a current $\mu$ can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed. By a construction...

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...