Self-dual manifolds and mirror symmetry for the quintic threefold

Abstract

For all $m>0$ we build a two-dimensional family of smooth manifolds of real dimension $3m+2$ and use it to interpolate between the anticanonical family in the complex projective space of dimension $m+1$ and its mirror dual. The main tool is the notion of self-dual manifold.

21 pages, no figures; in v2 corrected typo in Definition 2.1