Formation of a cusp of a branch curve (animation)
The two pictures below illustrate projecting the (affine cubic) surface
z^3 + x z + y = 0
to the (x,y) - plane. The branch curve in the (x,y) - plane, Delta = 27 y^2 + 16 x^3, which is a discriminant of this polynomial,
has an A_2 singularity. (In general, discriminant of an "universal polynomial" of degree d has singularity A_d-1)
(Both animations are made with the Surf program)
Semi-transparent:
Non-transparent:
