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

Nataliya Goncharuk; Yury Kudryashov

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arXiv · 1407.7878

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

Nataliya Goncharuk·Yury Kudryashov

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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.

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Nataliya Goncharuk, Yury Kudryashov. 2014-07-29. Genera of non-algebraic leaves of polynomial foliations of $\mathbb C^2$. https://arxiv.org/abs/1407.7878

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