We describe type IIB compactifications with varying coupling constant in
d=6,7,8,9 dimensions, where part of the ten-dimensional SL(2,Z) symmetry is
broken by a background with Gamma_0(n) or Gamma(n) monodromy for n=2,3,4. This
extends the known class of F-theory vacua to theories which are dual to
heterotic compactifications with reduced rank. On compactifying on a further
torus, we obtain a description of the heterotic moduli space of G bundles over
elliptically fibered manifolds without vector structure in terms of complex
geometries.
