We know every differential manifold can be triangulable. Let $M$ be a compact complex manifold of dimension $m$ and V be an analytic subset of dimension $s$ of $M.$ If $V$ has no singularity then $V$ is a compact complex submanifold of $M.$ Hence, V can be considered as an element of $H_{2s}(M,\mathbb{C})$ (singular homology of M) for $V$ can be triangulable and compact. Now, consider the general case when V has singularity, as far as I know in general V is not triangulable.

Besides, it is well-know that the analytic set $V$ has the Poincare duality $\omega$ in $H_{DR}^{2m-2s}(M)$ (De rham cohomology of $M$), and again $\omega$ has the Poincare duality $\sigma \in H_{2s}(M,\mathbb{C}).$ That means there exists $2s^{th}$ singular homology chain $\sigma$ such that for all 2s-form $\eta$ one has
$$\int_V \eta =\int_{\sigma} \eta.$$

Question: What is the geometric relation between $V$ and $\sigma$? On the other hand,

**How can $V$ be considered geometrically as an element of $H_{2s}(M,\mathbb{C})?$**