  We show that string theory on a compact negatively curved manifold,
preserving a U(1)^{b_1} winding symmetry, grows at least b_1 new effective
dimensions as the space shrinks. The winding currents yield a "D-dual"
description of a Riemann surface of genus h in terms of its 2h dimensional
Jacobian torus, perturbed by a closed string tachyon arising as a potential
energy term in the worldsheet sigma model. D-branes on such negatively curved
manifolds also reveal this structure, with a classical moduli space consisting
of a b_1-torus. In particular, we present an AdS/CFT system which offers a
non-perturbative formulation of such supercritical backgrounds. Finally, we
discuss generalizations of this new string duality.
