  We discuss local F-theory geometries and theirs gauge theory dualities in
terms of intersecting D7-branes wrapped four-cycles in Type IIB superstring.
The manifolds are built as elliptic K3 surface fibrations over intersecting
F_0=CP^1 \times CP^1 base geometry according to ADE Dynkin Diagrams. The base
is obtained by blowing up the extended ADE hyper-Kahler singularities of eight
dimensional manifolds considered as sigma model target spaces with eight
supercharges. The resulting gauge theory of such local F-theory models are
given in terms of Type IIB D7-branes wrapped intersecting F_0. The four
dimensional N=1 anomaly cancelation requirement translates into a condition on
the associated affine Lie algebras.
