  In this article, we prove two results. First, we construct a dense subset in
the space of polynomial foliations of degree $n$ such that each foliation from
this subset has a leaf with at least $\frac{(n+1)(n+2)}2-4$ handles. Next, we
prove that for a generic foliation invariant under the map $(x, y)\mapsto (x,
-y)$ all leaves have infinitely many handles.
