  We investigate a noncompact Gepner model, which is composed of a number of
SL(2,R)/U(1) Kazama-Suzuki models and N=2 minimal models. The SL(2,R)/U(1)
Kazama-Suzuki model contains the discrete series among the SL(2,R) unitary
representations as well as the continuous series. We claim that the discrete
series contain the vanishing cohomology and the vanishing cycles of the
associated noncompact Calabi-Yau manifold. We calculate the Elliptic genus and
the open string Witten indices. In the A_{N-1} ALE models, they actually agree
with the vanishing cohomology and the intersection form of the vanishing
cycles.
