Displaying similar documents to “Differential Equations associated to Families of Algebraic Cycles”

Mixed Hodge structure of affine hypersurfaces

Hossein Movasati (2007)

Annales de l’institut Fourier

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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 a Hodge cycle in regular fibers of f is given in terms of the vanishing of integrals of certain polynomial n -forms in ℂ n + 1 over topological...

Homology classes of real algebraic sets

Wojciech Kucharz (2008)

Annales de l’institut Fourier

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There is a large research program focused on comparison between algebraic and topological categories, whose origins go back to 1952 and the celebrated work of J. Nash on real algebraic manifolds. The present paper is a contribution to this program. It investigates the homology and cohomology classes represented by real algebraic sets. In particular, such classes are studied on algebraic models of smooth manifolds.