  We study some properties of a singular Landau-Ginzburg family characterized
by the multi-variable superpotential $W=-X^{-1}(Y_1Y_2)^{n-1} + {1\over n}
(Y_1Y_2)^n - Y_3Y_4$. We will argue that (the infra-red limit of) this theory
describes the topological degrees of freedom of the $c=1$ string compactified
at $n$ times the self-dual radius. We also briefly comment on the possible
realization of these line singularities as singularities of Calabi-Yau
manifolds.
