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On the Hodge conjecture for products of certain surfaces

J.J. Ramón Marí (2008)

Collectanea Mathematica

On the Hodge cycles of Prym varieties

Indranil Biswas (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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.

Siegmund Kosarew, Ingrid Bauer (1989)

Mathematische Annalen

On the hodge theory of the symmetric powers of a curve.

Sebastián del Baño (2002)

Publicacions Matemàtiques

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.

Osamu Hyodo (1986)

Journal für die reine und angewandte Mathematik

On the Infinitesimal Torelli Theorem for Certain irregular Surfaces of General Type.

Igor Reider (1988)

Mathematische Annalen

On the mixed Hodge structure associated to $π_{3}$ of a simply connected complex projective manifold

J. Carlson, H. Clemens, J. Morgan (1981)

Annales scientifiques de l'École Normale Supérieure

On the Mixed Hodge Structure on the Cohomology of the Milnor Fibre.

J. Scherk, J.H.M. Steenbrink (1985)

Mathematische Annalen

On the non-triviality of the Griffith group.

Stefan Müller-Stach (1992)

Journal für die reine und angewandte Mathematik

On the rationality of the period mapping

Andrew John Sommese (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On the Shafarevich and Tate conjectures for hyperkähler varieties.

Yves André (1996)

Mathematische Annalen

On the structure of Brieskorn lattice

Morihiko Saito (1989)

Annales de l'institut Fourier

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 $Ω_{X, 0}^{n + 1} / d f \land d Ω_{X, 0}^{n + 1}$ over $ℂ {{\partial_{t}^{- 1}}}$ such that the action of $t$ is expressed by $t v = A_{0} + A_{1} \partial_{t}^{- 1} v$ for two matrices $A_{0}, A_{1}$ with $A_{1}$ semi-simple, where $v =^{t} (v_{1} ... v_{μ})$ is the basis. As an application, we calculate the $b$ -function of $f$ in the case of two variables.

On the Torelli problem for kählerian $K - 3$ surfaces

Dan Burns, Michael Rapoport (1975)

Annales scientifiques de l'École Normale Supérieure

On the Torelli problem of Abelian complex Lie groups.

Erich Selder (1988)

Mathematica Scandinavica

On the weight filtration of the homology of algebraic varieties : the generalized Leray cycles

Fouad Elzein, András Némethi (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $Y$ be a normal crossing divisor in the smooth complex projective algebraic variety $X$ and let $U$ be a tubular neighbourhood of $Y$ in $X$ . Using geometrical properties of different intersections of the irreducible components of $Y$ , and of the embedding $Y \subset X$ , we provide the “normal forms” of a set of geometrical cycles which generate $H_{*} (A, B)$ , where $(A, B)$ is one of the following pairs $(Y, \emptyset)$ , $(X, Y)$ , $(X, X - Y)$ , $(X - Y, \emptyset)$ and $(\partial U, \emptyset)$ . The construction is compatible with the weights in $H_{*} (A, B, ℚ)$ of Deligne’s mixed Hodge structure. The main technical part...

On torsion in the slope spectral sequence

Richard Crew (1985)

Compositio Mathematica

On variation of Hodge-Tate structures.

Osamu Hyodo (1989)

Mathematische Annalen

Orbifold-Hodge numbers of Hilbert schemes

Lothar Göttsche (1996)

Banach Center Publications

Orbifolds, special varieties and classification theory

Frédéric Campana (2004)

Annales de l’institut Fourier

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

Frédéric Campana (2004)

Annales de l’institut Fourier

For any compact Kähler manifold $X$ and for any equivalence relation generated by a symmetric binary relation with compact analytic graph in $X \times X$ , 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 $X$ given in the previous paper of this fascicule, as well as in many other questions.

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