Construct an example: irreducible algebraic variety induces a reducible germ. This is another exercise of Daniel Huybrechts' book "Complex Geometry An Introduction". The question asks to construct examples of: 1\. Reducible variety induces an irreducible germ. 2\. Irreducible variety induces a reducible germ. For #1, I found that a variety $X=\\{0, 1\\}$ of two single points is reducible while at either point it induces an irreducible germ. For #2, can any one give an example?

The cusp $y^2=x^2+x^3$ in $\mathbb C^2$ is irreducible but has a reducible germ at the origin $(0,0)$.