Can one take quotient by finite group in the category of schemes? Will the singularities be visible? For example, it looks like $\mathbb{C}/\{z \sim -z\}$ is isomorphic to $\mathbb{C}$. What about complex analytic spaces - can we take quotients by finite groups and are the singularities visible?

Can one take quotient by finite group in the category of schemes? Will the singularities be visible? For example, it looks like $\mathbb{C}/\{z \sim -z\}$ is isomorphic to $\mathbb{C}$. What about complex analytic spaces - can we take quotients by finite groups and are the singularities visible?

From the comments, I know that quotient singularities are visible on schemes/analytic spaces of complex dimension $\geq 2$. Are there examples of quotient singularities on curves?