  We study the relation between phenomenological requirements and the topology
of the surfaces that GUT 7-branes wrap in F-theory compactifications. In
addition to the exotic matter free condition in the hypercharge flux scenario
of SU(5)_{GUT} breaking, we analyze a new condition that comes from a discrete
symmetry aligning the contributions to low-energy Yukawa matrices from a number
of codimension-three singularity points. We see that the exotic matter free
condition excludes Hirzebruch surfaces (except ${\mathbb F}_0$) as the GUT
surface, correcting an existing proof in the literature. We further find that
the discrete symmetry for the alignment of the Yukawa matrices excludes del
Pezzo surfaces and a rational elliptic surface as the GUT surface. Therefore,
some GUT 7-brane surfaces are good for some phenomenological requirements, but
sometimes not for others, and this aspect should be kept in mind in geometry
search in F-theory compactifications.
