- Published 2006

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 over topological n-cycles on the fibers of f . Since the n-th homology of a regular fiber is generated by vanishing cycles, this leads us to study Abelian integrals over them. Our result generalizes and uses the arguments of J. Steenbrink in [St77] for quasi-homogeneous polynomials.

@inproceedings{Movasati2006MixedHS,
title={Mixed Hodge structure of affine hypersurfaces},
author={Hossein Movasati},
year={2006}
}