The topological Euler characteristic of a smooth algebraic curve of genus $g$ equals $2-2g$.
Let $C=\bigcup_{i=1}^n C_i$ be a union of smooth algebraic curves. I am wondering if there is a way to compute the topological Euler characteristic of $C$ in terms of the topological Euler characteristics of $C_i$, $i\in \{1,\cdots,n\}$.
I am assuming that the union is not necessarily disjoint and that the intersections may not be transversal.