Symmetries on the space of (2,2) superstring vacua and automorphism groups of Calabi-Yau manifolds

Symmetry groups on the space of (2,2) string vacua for c = 3, 6, and 9 are discussed in the context of orbifoldized Landau-Ginzburg theories. A general method for finding the maximal symmetry groups on the moduli space of untwisted marginal operators is presented by studying symmetries on the resolution of isolated singularities of superpotentials. Stabilizing subgroups of such symmetry groups are shown to correspond with automorphism groups of Calabi-Yau manifolds. In addition to our earlier work on this subject, we present some new examples for c = 9 (2,2) vacua. Subsequently we discuss modular transformations that relate small volume target-spaces to large ones.