Algebraic description of G-flux in F-theory: new techniques for F-theory   phenomenology
  We give a global algebraic description of the four-form flux in F-theory. We present how to compute its D3-tadpole and how to calculate the number of four-dimensional chiral states at the intersection of 7-branes directly in F-theory. We check that, in the weak coupling limit, we obtain the same results as using perturbative type IIB string theory. We develop these techniques in full generality. However, they can be readily applied to concrete models, as we show in an explicit example. 
A. P. Braun, A. Collinucci and R. Valandro
hep-th math.AG