For all m greater than or equal to 1 we build a two-dimensional family of smooth manifolds of real dimension 3m + 2 and use it to interpolate between the anticanonical family in CPm +1 and its mirror dual. The main tool is the notion of self-dual manifolds.
"Self-Dual Manifolds and Mirror Symmetry for the Quintic Threefold." Asian J. Math. 9 (1) 079 - 102, March, 2005.