We prove f-positivity of Ox (1) for arbitrary dimensional fibrations over curves f:X¿B whose general fibre is a complete intersection. In the special case where the family is a global complete intersection, we prove numerical ...

Let $\pi :S\longrightarrow B$ be a bielliptic fibration. We prove $S$ is, up to base change, a rational double cover of an elliptic fibration and that $\pi $ is isotrivial provided it is smooth. Finally, we prove that the ...

We study the topological index of some irregular surfaces that we call generalized Lagrangian. We show that under certain hypotheses on the base locus of the Lagrangian system the topological index is non-negative. For ...

We study and obtain Slope inequalities for fibred irregular varieties of non-maximal Albanese dimension. We give a comparison theorem between Clifford–Severi and Slope inequalities for this type of fibrations. We also ...

We study relative hypersurfaces, and prove an instability condition for the fibres. This is the starting point for an investigation of the geometry of effective divisors on relative projective bundles.

Let Xbe a smooth complex projective variety such that the Albanese map of Xis generically ¿nite onto its image. Here we study the so-called eventual m-paracanonical map of X, whose existence is implied by the results of ...