Past exam of the geometry course of the University of Oxford / 2010 / B / 5 / d / Solution

Take the union of $n$ distinct projective lines in general position, with no three concurrent. Its defining polynomial is the product of their linear equations, so its degree is $n$. Exactly two lines meet at each of the $\left(\genfrac{}{}{0ex}{}{n}{2}\right)$ pairwise intersections, producing an ordinary double point; elsewhere just one line passes through and the curve is smooth. HenceFor $n=1$, the line itself gives zero singular points, as required.