Volume 18, issue 3 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A mirror theorem for the mirror quintic

Yuan-Pin Lee and Mark Shoemaker

Geometry & Topology 18 (2014) 1437–1483
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/