  We discuss two-dimensional sigma models on moduli spaces of instantons on K3
surfaces. These N=(4,4) superconformal field theories describe the near-horizon
dynamics of the D1-D5-brane system and are dual to string theory on AdS_3. We
derive a precise map relating the moduli of the K3 type IIB string
compactification to the moduli of these conformal field theories and the
corresponding classical hyperkaehler geometry. We conclude that, in the absense
of background gauge fields, the metric on the instanton moduli spaces
degenerates exactly to the orbifold symmetric product of K3. Turning on a
self-dual NS B-field deforms this symmetric product to a manifold that is
diffeomorphic to the Hilbert scheme. We also comment on the mathematical
applications of string duality to the global issues of deformations of
hyperkaehler manifolds.
