Resumen de New slope inequalities for families of complete intersections

Miguel Ángel Barja Yáñez , Lidia Stoppino

• 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 sufficient and necessary conditions for f-positivity of powers of OX(1) and for the relative canonical sheaf. From these results we also derive a Chow instability condition for the fibres of relative complete intersections in the projective bundle of a μ-unstable bundle.