Donu Arapura

The first result, which is bit technical to state, is a strong topological restriction on  "large" fundamental groups of smooth complex projective varieties. The second is a calculation of the Mumford-Tate group of an etale cover of a generic curve. These seeming unrelated results were both motivated by the same question: Given a projective map of complex varieties, what sorts of restrictions are there for the (outer) action of the fundamental group of the base on the fundamental group of the general fibre or on the kernel?