  We apply the nonlinear steepest descent method to a class of 3x3
Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix
random model. The general case of two equilibrium measures supported on an
arbitrary number of intervals is considered. In this case, we solve the
Riemann-Hilbert problem for the outer parametrix in terms of sections of a
spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and
establish strong asymptotic results for the Cauchy biorthogonal polynomials.
