A mysterious duality

We establish a correspondence between toroidal compactifications of M-theory and del Pezzo surfaces. M-theory on T k corresponds to P 2 blown up at k generic points; Type IIB corresponds to P 1 x P 1 . The moduli of compactifications of M-theory on rectangular tori are mapped to Kahler moduli of del Pezzo surfaces. The U-duality group of Mtheory corresponds to a group of classical symmetries of the del Pezzo represented by global diffeomorphisms. The |-BPS brane charges of M-theory correspond to spheres in the del Pezzo, and their tension to the exponentiated volume of the corresponding spheres. The electric/magnetic pairing of branes is determined by the condition that the union of the corresponding spheres represent the anticanonical class of the del Pezzo. The condition that a pair of |-BPS states form a bound state is mapped to a condition on the intersection of the corresponding spheres. We present some speculations about the meaning of this duality.