From local to global in F-theory model building

When locally engineering F-theory models some D7D7-branes for the gauge group factors are specified and matter is localized on the intersection curves of the compact parts of the world-volumes. In this note, we discuss to what extent one can draw conclusions about F-theory models by just restricting the attention locally to a particular seven-brane. Globally, the possible D7D7-branes are not independent from each other and the (compact part of the) D7D7-brane can have unavoidable intrinsic singularities. Many special intersecting loci which were not chosen by hand occur inevitably, notably codimension-three loci which are not   intersections of matter curves. We describe these complications specifically in a global SU(5)SU(5) model and also their impact on the tadpole cancellation condition.