Notes on a singular Landau-Ginzburg family

We study some properties of a singular Landau-Ginzburg family characterized by the multi-variable superpotential W = −X−1(Y1Y2)n−1 + 1n(Y1Y2)n − Y3Y4. 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.