  We revisit a correspondence between toroidal compactifications of M-theory
and del Pezzo surfaces, in which rational curves on the del Pezzo are related
to ${1\over 2}$-BPS branes of the corresponding compactification. We argue that
curves of higher genus correspond to non-geometric backgrounds of the M-theory
compactifications, which are related to exotic branes. In particular, the
number of "special directions" of the exotic brane is equal to the genus of the
corresponding curve. We also point out a relation between addition of curves in
the del Pezzo and the brane polarization effect.
