A mirror theorem for the mirror quintic

Lee, Yuan-Pin; Shoemaker, Mark

doi:10.2140/gt.2014.18.1437

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

A mirror theorem for the mirror quintic

Yuan-Pin Lee and Mark Shoemaker

Geometry & Topology 18 (2014) 1437–1483

DOI: 10.2140/gt.2014.18.1437

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.

Keywords

mirror symmetry, mirror theorem

Mathematical Subject Classification 2010

Primary: 14N35

Secondary: 53D45

References

Publication

Received: 5 November 2013

Accepted: 17 January 2014

Published: 7 July 2014

Proposed: Jim Bryan

Seconded: Richard Thomas, Yasha Eliashberg

Authors

Yuan-Pin Lee
Department of Mathematics University of Utah 155 S 1400 E Room 233 Salt Lake City, UT 84112-0090 USA
http://www.math.utah.edu/~yplee/
Mark Shoemaker
Department of Mathematics University of Utah 155 S 1400 E Room 233 Salt Lake City, UT 84112-0090 USA
http://www.math.utah.edu/~markshoe/

Volume 18, issue 3 (2014)