 
Summary: Problem Set 17
There was a typo on Problem 4 from Problem Set 16. It should read as:
Problem 1. Let C be the non singular cubic curve in P2
determined by the
equation y2
z = x3
+ ax2
z + bxz2
+ cz3
. Let 0 = [0 : 1 : 0]. Let Pi = [xi : yi : 1] for
i = 1, 2, 3. Suppose P1 P2 = P3. If x1 = x2 then let = (y1  y2)/(x1  x2). If
P1 = P2 and y1 = 0, let = (3x2
1 + 2ax1 + b)/(2y1). Let µ = yi  xi (for i = 1
or 2). Show that x3 = 2
 a  x1  x2 and y3 = x3  µ.
Problem 5 (and problem 6 with a bit of work) of the previous problem set
can be done without the aid of the problem above. It can even be done on the
computer by using ideal quotients.
Problem 2. Let C be an irreducible cubic. Let L be a line such that L · C =
P1 + P2 + P3 with the Pi distinct. Let Li be the tangent line to C at Pi (So
