Hossein Movasati

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The aim of this paper is to introduce the theory of Abelian integrals for holomorphic foliations in a complex manifold of dimension two. We will show the importance of Picard-Lefschetz theory and the classification of relatively exact 1-forms in this theory. As an application we identify some irreducible components of the space of holomorphic foliations of(More)
The main objective of this article is to study the topology of the fibers of a generic rational function of the type F p Gq 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 Gq . In particular, we will prove that(More)
In this article we introduce algorithms which compute iterations of Gauss-Manin connections, Picard-Fuchs equations of Abelian integrals and mixed Hodge structure of affine varieties of dimension n in terms of differential forms. In the case n = 1 such computations have many applications in differential equations and counting their limit cycles. For n > 3,(More)
In this article we give an algorithm which produces a basis of the n-th de Rham cohomology of the affine smooth hypersurface f−1(t) compatible with the mixed Hodge structure, where f is a polynomial in n+ 1 variables and satisfies a certain regularity condition at infinity (and hence has isolated singularities). As an application we show that the notion of(More)