# Moscow Mathematical Journal

Volume 18, Issue 1, January–March 2018 pp. 63–83.

Genera of Non-Algebraic Leaves of Polynomial Foliations of ℂ^{2}

**Authors**:
Nataliya Goncharuk (1) and Yury Kudryashov (1)

**Author institution:**(1) Higher School of Economics, Department of Mathematics, 20 Myasnitskaya street, Moscow 101000, Russia

Cornell University, College of Arts and Sciences, Department of Mathematics, 310 Mallot Hall, Ithaca, NY, 14853, US

**Summary: **

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 (except for a finite set of algebraic leaves) have infinitely many handles.

2010 Math. Subj. Class. Primary: 37F75; Secondary: 32M25.

**Keywords:**Riemann surfaces, complex foliations, polynomial foliations, complex limit cycles.

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