  We present the theory describing supersymmetrical vortices in the curved
superspace of the (1,0) supergravity. The action is defined as a (1,0) locally
supersymmetric $SU(2)/U(1)$ coset perturbed by the cosmological constant-like
term. The perturbation is such that it preserves the integrability of the coset
model. Because of supersymmetry the perturbed theory is an exact quantum system
provided a proper dilaton is taken into account. The exact value of the dilaton
is determined in the supersymmetric case by the quasi-classical background of
the bosonic coset.
