Displaying similar documents to “Orbifold-Hodge numbers of Hilbert schemes”

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...

Differential Equations associated to Families of Algebraic Cycles

Pedro Luis del Angel, Stefan Müller-Stach (2008)

Annales de l’institut Fourier

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We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (, motivic cohomology groups). This formalism is related to inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.

Albanese varieties with modulus and Hodge theory

Kazuya Kato, Henrik Russell (2012)

Annales de l’institut Fourier

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Let X be a proper smooth variety over a field k of characteristic 0 and Y an effective divisor on X with multiplicity. We introduce a generalized Albanese variety Alb ( X , Y ) of X of modulus Y , as higher dimensional analogue of the generalized Jacobian with modulus of Rosenlicht-Serre. Our construction is algebraic. For k = ℂ we give a Hodge theoretic description.