  We consider the boundary dual of AdS3xS3xK3 for NS5-flux Q5=1, which is
described by a sigma model with target space given by the d-fold symmetric
product of K3. Building on results in algebraic geometry, we address the
problem of deforming it away from the orbifold point from the viewpoint of
topological strings. We propose how the 't Hooft expansion can be geometrized
in terms of Gromov-Witten invariants and, in favorable settings, how it can be
summed up to all orders in closed form. We consider an explicit example in
detail for which we discuss the genus expansion around the orbifold point, as
well as the divergence in the strong coupling regime. We find that within the
domain of convergence, scale separation does not occur. However, in order for
the mathematical framework to be applicable in the first place, we need to
consider "reduced" Gromov-Witten invariants that fit, as we argue, naturally to
topologically twisted N=4 strings. There are some caveats and thus to what
extent this toy model captures the physics of strings on AdS3xS3xK3 remains to
be seen.
