  The string landscape satisfies interesting finiteness properties imposed by
supersymmetry and string-theoretical consistency conditions. We study N=1
supersymmetric compactifications of Type IIB string theory on smooth
elliptically fibered Calabi-Yau threefolds at large volume with magnetized
D9-branes and D5-branes. We prove that supersymmetry and tadpole cancellation
conditions imply that there is a finite number of such configurations. In
particular, we derive an explicitly computable bound on the number of magnetic
flux quanta, as well as the number of D5-branes, which is independent of the
continuous moduli of the setup. The proof applies if a number of easy to check
geometric conditions of the twofold base are met. We show that these geometric
conditions are satisfied for the almost Fano twofold bases given by each toric
variety associated to a reflexive two-dimensional polytope as well as by the
generic del Pezzo surfaces dP_n with n=0,...,8. Physically, this finiteness
proof shows that there exist a finite collection of four-dimensional gauge
groups and chiral matter spectra in the 4D supergravity theories realized by
these compactifications. As a by-product we explicitly construct all generators
of the Kaehler cones of dP_n and work out their relation to representation
theory.
