BRANES AT ANGLES AND BLACK-HOLES

We construct the most general supersymmetric configuration of D2-brane s and D6-branes on a 6-torus. It contains arbitrary numbers of branes at relative U(3) angles. The corresponding supergravity solutions are constructed and expressed in a remarkably simple form, using the compl ex geometry of the compact space. The spacetime supersymmetry of the c onfiguration is verified explicitly, by solution of the Killing spinor equations, and the equations of motion are verified too. Our configur ations can be interpreted as a 16-parameter family of regular extremal black holes in four dimensions. Their entropy is interpreted microsco pically by counting the degeneracy of bound states of D-branes. Our re sult agrees in detail with the prediction for the degeneracy of BPS st ates in terms of the quartic invariant of the E(7,7) duality group.