A mirror theorem for the mirror quintic

Abstract

The celebrated Mirror theorem states that the genus zero part of the $A$ model (quantum cohomology, rational curves counting) of the Fermat quintic threefold is equivalent to the $B$ model (complex deformation, variation of Hodge structure) of its mirror dual orbifold. In this article, we establish a mirror-dual statement. Namely, the $B$ model of the Fermat quintic threefold is shown to be equivalent to the $A$ model of its mirror, and hence establishes the mirror symmetry as a true duality.