Tangent-space obstruction between two unions of three lines
= Tangent-space obstruction between two unions of three lines
The union of the three coordinate axes in $\mathbb A^3$ and a union of three distinct lines through the origin in $\mathbb A^2$ are not <isomorphism of algebraic varieties>[isomorphic]. Their origins are intrinsically the unique points common to all three <irreducible components>, but their <Zariski tangent space>[Zariski tangent spaces] there have dimensions three and two respectively.