On Grothendieck's generalized Hodge conjecture for a family of threefolds with trivial canonical bundle.
On Hodge structures and non-representability of Chow groups
On the de Rham-Witt complex attached to a semi-stable family
On the genus of reducible surfaces and degenerations of surfaces
We deal with a reducible projective surface with so-called Zappatic singularities, which are a generalization of normal crossings. First we compute the -genus of , i.e. the dimension of the vector space of global sections of the dualizing sheaf . Then we prove that, when is smoothable, i.e. when is the central fibre of a flat family parametrized by a disc, with smooth general fibre, then the -genus of the fibres of is constant.
On the Hodge spectral sequence for some classes of non-complete algebraic manifolds.
On the period map for abelian covers of projective varieties
On the variational Torelli problem for complete intersections