  Let $f$ be a plane curve. We give a procedure based on Abhyankar's
approximate roots to detect if it has a single place at infinity, and if so
construct its associated $\delta$-sequence, and consequently its value
semigroup. Also for fixed genus (equivalently Frobenius number) we construct
all $\delta$-sequences generating numerical semigroups with this given genus.
For a $\delta$-sequence we present a procedure to construct all curves having
this associated sequence.
  We also study the embeddings of such curves in the plane. In particular, we
prove that polynomial curves might not have a unique embedding.
