Hochschild cohomology of complex spaces and Noetherian schemes.
Hodge classes on self-products of a variety with an automorphism
Hodge conjecture for cubic 8-folds.
Hodge filtrations and the higher direct images of canonical sheaves.
Hodge groups of K3 surfaces.
Hodge integrals and invariants of the unknot.
Hodge metrics and the curvature of higher direct images
Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.
Hodge modules on Shimura varieties and their higher direct images in the Baily–Borel compactification
Hodge numbers attached to a polynomial map
We attach a limit mixed Hodge structure to any polynomial map . The equivariant Hodge numbers of this mixed Hodge structure are invariants of which reflect its asymptotic behaviour. We compute them for a generic class of polynomials in terms of equivariant Hodge numbers attached to isolated hypersurface singularities and equivariant Hodge numbers of cyclic coverings of projective space branched along a hypersurface. We show how these invariants allow to determine topological invariants of such...
Hodge numbers of a double octic with non-isolated singularities
If B is a surface in ℙ³ of degree 8 which is the union of two smooth surfaces intersecting transversally then the double covering of ℙ³ branched along B has a non-singular model which is a Calabi-Yau manifold. The aim of this note is to compute the Hodge numbers of this manifold.
Hodge spaces of real toric varieties
Hodge Spectral Sequence on Pseudoconvex Domains.
Hodge theory and deformations of maps
Hodge type of projective varieties of low degree.
Hodge type of subvarieties of compact hermitian symmetric spaces.
Hodge type of subvarieties of IPn of small degrees.
Hodge-gaussian maps
Hodge-Tate and de Rham representations in the imperfect residue field case
Let be a -adic local field with residue field such that and be a -adic representation of . Then, by using the theory of -adic differential modules, we show that is a Hodge-Tate (resp. de Rham) representation of if and only if is a Hodge-Tate (resp. de Rham) representation of where is a certain -adic local field with residue field the smallest perfect field containing .
Hodge-Tate periods and p-adic abelian integrals.
Hodge-Tate Structures and Modular Forms.