 Solution

ID: 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

(2 n)

pairwise intersections, producing an ordinary double point; elsewhere just one line passes through and the curve is smooth. Hence

# Sing (C) = (2 n) = \frac{1}{2} n (n - 1) .

For

n = 1

, the line itself gives zero singular points, as required.

 New to topics? Read the docs here!