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Genera of non-algebraic leaves of polynomial foliations of $\mathbb C^2$
Nataliya Goncharukab, Yury Kudryashovab a Higher School of Economics, Department of Mathematics, 20 Myasnitskaya street, Moscow 101000, Russia
b Cornell University, College of Arts and Sciences, Department of Mathematics, 310 Mallot Hall, Ithaca, NY, 14853, US
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 (except for a finite set of algebraic leaves) have infinitely many handles.
Key words and phrases:
Riemann surfaces, complex foliations, polynomial foliations, complex limit cycles.
Citation:
Nataliya Goncharuk, Yury Kudryashov, “Genera of non-algebraic leaves of polynomial foliations of $\mathbb C^2$”, Mosc. Math. J., 18:1 (2018), 63–83
Linking options:
https://www.mathnet.ru/eng/mmj662 https://www.mathnet.ru/eng/mmj/v18/i1/p63
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Abstract page: | 167 | References: | 32 |
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