  We use Morse theoretical arguments to study algebraic curves in C^2. We take
an algebraic curve C in C^2 and intersect it with a family of spheres with
fixed origin and varying radii. We explain in detail how does the resulting
link change when we cross a singular point of C. Applying link invariants as
Murasugi's signature and Levine--Tristram signatures we obtain some
informations about possible singularities of a curve C in terms of its
topology.
