Geometric variations of local systems and elliptic surfaces

Geometric variations of local systems are families Hodge structure; they typically correspond to fibrations Kähler manifolds for which each fibre itself is fibred by codimension one manifolds. In this article, we introduce the formalism geometric and then specialize theory study elliptic surfaces. We interpret a construction twisted surface used Besser—Livné in terms middle convolution functor, use explicit methods calculate structure underlying universal MN-polarized K3 Finally, explain connection between isomonodromic deformations, were originally considered first author 1999.