Genera of non-algebraic leaves of polynomial foliations of $mathbb C^2$

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.

Genera of non-algebraic leaves of polynomial foliations of $mathbb C^2$ Institutional Repository Document