Affine plane with doubled origin
= Affine plane with doubled origin
The affine plane with doubled origin is formed by gluing two copies of $\mathbb A_k^2$ by the identity away from the origin. The overlap is the <punctured affine plane>, so this scheme is nonseparated and the two-open affine cover is not acyclic for the structure sheaf.
The gluing resembles a <non-Hausdorff manifold> example, but this node concerns an algebraic scheme and its nonseparatedness, not a real manifold.