Mordell-Weil lattice via string junctions

We analyze the structure of singularities, Mordell-Weil lattices and torsio ns of a rational elliptic surface using string junctions in the background of 12 7-branes. The classification of the Mordell-Weil lattices due to Ogui so-Shioda is reproduced in terms of the junction lattice. In this analysis an important role played by the global structure of the surface is observed . It is then found that the torsions in the Mordell-Weil group are generate d by the fraction of loop junctions which represent the imaginary roots of the loop algebra (E) over cap(9). From the structure of the Mordell-Weil la ttice we find 7-brane configurations which support non-BPS junctions carryi ng conserved Abelian charges. (C) 2000 Elsevier Science B.V. All rights res erved.