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

Abstract

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.

Cited by in corpus (1)

• Topology of leaves of generic logarithmic foliations on ${\mathbb{CP}}^2$