CONSTRUCTION AND COUPLINGS OF MIRROR MANIFOLDS

We present an analysis of the conjectured existence of Calabi-Yau "mirror manifolds" for the case where the starting manifold is Y4,5. We construct mirror pairs with equal but opposite values for the Euler characteristic and the Hodge numbers h2,1 and h1,1 interchanged. In one particular example we show that the couplings of (1,1)-forms equal the couplings of (2,1)-forms in the mirror manifold, provided that a suitable limit is taken of the complex structure which corresponds to the large-radius limit appropriate for the mirror manifold. This leads to a determination, via deformation theory, of corrections to the topologically determined couplings of the (1,1)-forms. © 1990.