From Local to Global in F-Theory Model Building

When locally engineering F-theory models some D7-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 D7-branes are not independent from each other and the (compact part of the) D7-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) model and also their impact on the tadpole cancellation condition.