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Working paper

Genera of non-algebraic leaves of polynomial foliations of ℂ²

arxiv.org. math. Cornell University, 2014. No. 1407.7878.
Nataliya Goncharuk, Kudryashov Y.
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 (n+1)(n+2)/2-4 handles. Next, we prove that for a generic foliation invariant under the map (x, y) ↦ (x, -y) all leaves have infinitely many handles.