Perturbation of the ground varieties of c=1 string theory

Abstract

We discuss the effect of perturbations on the ground rings of c=1 string theory at the various compactification radii defining the A_N points of the moduli space. We argue that perturbations by plus-type moduli define ground varieties which are equivalent to the unperturbed ones under redefinitions of the coordinates and hence cannot smoothen the singularity. Perturbations by the minus-type moduli, on the other hand, lead to semi-universal deformations of the singular varieties that can smoothen the singularity under certain conditions. To first order, the cosmological perturbation by itself can remove the singularity only at the self-dual (A₁) point.