  We show that quantum curves arise in infinite families and have the structure
of singular vectors of a relevant symmetry algebra. We analyze in detail the
case of the hermitian one-matrix model with the underlying Virasoro algebra,
and the super-eigenvalue model with the underlying super-Virasoro algebra. In
the Virasoro case we relate singular vector structure of quantum curves to the
topological recursion, and in the super-Virasoro case we introduce the notion
of super-quantum curves. We also discuss the double quantum structure of the
quantum curves and analyze specific examples of Gaussian and multi-Penner
models.
