Aspinwall, PS; Greene, BR; Morrison, DR, *The Monomial-Divisor Mirror Map*,
Internat. Math. Res. Notices (1993), 319-337, vol. 72 no. 3
(September, 1993),
pp. 319 -- 337 [9309007v1] .
**Abstract:**

*For each family of Calabi-Yau hypersurfaces in toric varieties, Batyrev has
proposed a possible mirror partner (which is also a family of Calabi-Yau
hypersurfaces). We explain a natural construction of the isomorphism between
certain Hodge groups of these hypersurfaces, as predicted by mirror symmetry,
which we call the monomial-divisor mirror map. We indicate how this map can be
interpreted as the differential of the expected mirror isomorphism between the
moduli spaces of the two Calabi-Yau manifolds. We formulate a very precise
conjecture about the form of that mirror isomorphism, which when combined with
some earlier conjectures of the third author would completely specify it. We
then conclude that the moduli spaces of the nonlinear sigma models whose
targets are the different birational models of a Calabi-Yau space should be
connected by analytic continuation, and that further analytic continuation
should lead to moduli spaces of other kinds of conformal field theories. (This
last conclusion was first drawn by Witten.)*