  We construct modular invariant partition functions for type II strings on a
conifold and a singular Eguchi-Hanson instanton by means of the SL(2,R)/U(1)
version of Gepner models. In the conifold case, we find an extra massless
hypermultiplet in the IIB spectrum and argue that it may be identified as a
soliton. In the Eguchi-Hanson case, our formula is new and different from the
earlier result, in particular does not contain graviton. The lightest IIB
fields are combined into a six-dimensional (2,0) tensor multiplet with a
negative mass square. We give an interpretation to it as a doubleton-like mode.
