On the Topology of Foliations with a First Integral

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dc.creatorMovasati, Hossein
dc.date2002-06-07
dc.date.accessioned2026-07-07T04:48:58Z
dc.date.available2026-07-07T04:48:58Z
dc.descriptionThe main objective of this article is to study the topology of the fibers of a generic rational function of the type $F^p/G^q$ in the projective space of dimension two. We will prove that the action of the monodromy group on a single Lefschetz vanishing cycle $δ$ generates the first homology group of a generic fiber of $F^p/G^q$. In particular, we will prove that for any two Lefschetz vanishing cycles $δ_0$ and $δ_1$ in a regular compact fiber of $F^p/G^q$, there exists a monodromy $h$ such that $h(δ_0)=\pm δ_1$.
dc.description31 pages
dc.identifierhttps://arxiv.org/abs/math/0206075
dc.identifierhttp://arxiv.org/abs/math/0206075
dc.identifierBol. Soc. Brasil. Mat. (N.S.) 31 (2000), no. 3, 305-336
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64252
dc.subjectGeometric Topology
dc.subjectAlgebraic Geometry
dc.subject14D99; 57R30
dc.titleOn the Topology of Foliations with a First Integral
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