Displaying similar documents to “Mixed Hodge structure of affine hypersurfaces”

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.

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.

Spectrum and multiplier ideals of arbitrary subvarieties

Alexandru Dimca, Philippe Maisonobe, Morihiko Saito (2011)

Annales de l’institut Fourier

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We introduce a spectrum for arbitrary subvarieties. This generalizes the definition by Steenbrink for hypersurfaces. In the isolated complete intersection singularity case, it coincides with the one given by Ebeling and Steenbrink except for the coefficients of integral exponents. We show a relation to the graded pieces of the multiplier ideals by using the filtration V of Kashiwara and Malgrange. This implies a partial generalization of a theorem of Budur in the hypersurface case. The...

Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces

Klaus Hulek, Remke Kloosterman (2011)

Annales de l’institut Fourier

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In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted projective 4 -space. We then give a method for calculating the cohomology of a certain class of singular hypersurfaces, extending work of Dimca for the isolated singularity case.