The Pfaffian Calabi–Yau, its Mirror, and their Link to the Grassmannian G(2,7)

The rank 4 locus of a general skew-symmetric 7 × 7 matrix gives the Pfaffian variety in P 20 which is not defined as a complete intersection. Intersecting this with a general P 6 gives a Calabi–Yau manifold. An orbifold construction seems to give the 1-parameter mirror-family of this. However, corresponding to two points in the 1-parameter family of complex structures, both with maximally unipotent monodromy, are two different mirror-maps: one corresponding to the general Pfaffian section, the other to a general intersection of G (2,7) ⊂ P 20 with a P 13 . Apparently, the Pfaffian and G (2,7) sections constitute different parts of the A-model (Kähler structure related) moduli space, and, thus, represent different parts of the same conformal field theory moduli space.