## Geometry & Topology

### 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.

#### Article information

Source
Geom. Topol., Volume 18, Number 3 (2014), 1437-1483.

Dates
Accepted: 17 January 2014
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732799

Digital Object Identifier
doi:10.2140/gt.2014.18.1437

Mathematical Reviews number (MathSciNet)
MR3228456

Zentralblatt MATH identifier
1305.14025

Keywords
mirror symmetry mirror theorem

#### Citation

Lee, Yuan-Pin; Shoemaker, Mark. A mirror theorem for the mirror quintic. Geom. Topol. 18 (2014), no. 3, 1437--1483. doi:10.2140/gt.2014.18.1437. https://projecteuclid.org/euclid.gt/1513732799

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