On the Hodge conjecture for products of certain surfaces
On the Hodge cycles of Prym varieties
We show that the Néron–Severi group of the Prym variety for a degree three unramified Galois covering of a hyperelliptic Riemann surface has a distinguished subgroup of rank three. For the general hyperelliptic curve, the algebra of Hodge cycles on the Prym variety is generated by this group of rank three.
On the Hodge spectral sequence for some classes of non-complete algebraic manifolds.
On the hodge theory of the symmetric powers of a curve.
We describe the polarised Hodge structure on the symmetric powers of a smooth projective curve.
On the Hodge-Tage decomposition in the imperfect residue field case.
On the Infinitesimal Torelli Theorem for Certain irregular Surfaces of General Type.
On the mixed Hodge structure associated to of a simply connected complex projective manifold
On the Mixed Hodge Structure on the Cohomology of the Milnor Fibre.
On the non-triviality of the Griffith group.
On the rationality of the period mapping
On the Shafarevich and Tate conjectures for hyperkähler varieties.
On the structure of Brieskorn lattice
We study the structure of the filtered Gauss-Manin system associated to a holomorphic function with an isolated singularity, and get a basis of the Brieskorn lattice over such that the action of is expressed byfor two matrices with semi-simple, where is the basis. As an application, we calculate the -function of in the case of two variables.
On the Torelli problem for kählerian surfaces
On the Torelli problem of Abelian complex Lie groups.
On the weight filtration of the homology of algebraic varieties : the generalized Leray cycles
Let be a normal crossing divisor in the smooth complex projective algebraic variety and let be a tubular neighbourhood of in . Using geometrical properties of different intersections of the irreducible components of , and of the embedding , we provide the “normal forms” of a set of geometrical cycles which generate , where is one of the following pairs , , , and . The construction is compatible with the weights in of Deligne’s mixed Hodge structure. The main technical part...
On torsion in the slope spectral sequence
On variation of Hodge-Tate structures.
Orbifold-Hodge numbers of Hilbert schemes
Orbifolds, special varieties and classification theory
This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds. We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres. We next show that rationally connected Kähler...
Orbifolds, special varieties and classification theory: an appendix
For any compact Kähler manifold and for any equivalence relation generated by a symmetric binary relation with compact analytic graph in , the existence of a meromorphic quotient is known from Inv. Math. 63 (1981). We give here a simplified and detailed proof of the existence of such quotients, following the approach of that paper. These quotients are used in one of the two constructions of the core of given in the previous paper of this fascicule, as well as in many other questions.