  We give two proofs of a conjecture of the first author (Inv. Math. 98, 1989)
that a reduced algebraic plane curve is regular at infinity if and only if its
link at infinity is a regular toral link. This conjecture has also been proved
by Ha H.~V. using Lojasiewicz numbers at infinity. Our first proof uses the
polar invariant and the second proof uses linear systems of plane curve
singularities. The second approach (based on a paper in preparation) also
proves a stronger conjecture (loc. cit.) describing topologically the regular
link at infinity associated with an irregular link at infinity.

Algebraic Geometry;Algebraic Geometry