Higgs bundles and local systems
Higher asymptotics of the complex Monge-Ampère equation
Higher de Rham-Witt complexes of supersingular K3 surfaces
Higher degree Galois covers of .
Higher direct images of canonical sheaves tensorized with semi-positive vector bundles by proper Kähler morphisms.
Higher order modular forms and mixed Hodge theory
Higher-Dimensional Analogues of Inoue-Hirzebruch Surfaces.
Hilbert spaces for massless particles with nonvanishing helicities
Hilbert-Samuel Polynomials of a Proper Morphism.
Hilbert-Schmidt Hankel operators with anti-holomorphic symbols on complete pseudoconvex Reinhardt domains
On complete pseudoconvex Reinhardt domains in , we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman space is infinite...
Hilbert-valued forms and barriers on weakly pseudoconvex domains.
We introduce an alternative proof of the existence of certain Ck barrier maps, with polynomial explosion of the derivatives, on weakly pseudoconvex domains in Cn. Barriers of this sort have been constructed very recently by J. Michel and M.-C. Shaw, and have various applications. In our paper, the adaptation of Hörmander's L2 techniques to suitable vector-valued functions allows us to give a very simple approach of the problem and to improve some aspects of the result of Michel and Shaw, regarding...
Hinfty + LE in several variables.
Hirzebruch's conjecture on cusp singularities.
Hochschild cohomology of complex spaces and Noetherian schemes.
Hodge groups of K3 surfaces.
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 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 Spectral Sequence on Pseudoconvex Domains.
Hodge theory for twisted differentials
We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class C of Fujiki. We give a Hodgetheoretical proof of the characterization of solvmanifolds in class C of Fujiki, first stated by D. Arapura.
Hodge type of subvarieties of compact hermitian symmetric spaces.