Volume 18, issue 3 (2014)

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A mirror theorem for the mirror quintic

Yuan-Pin Lee and Mark Shoemaker

Geometry & Topology 18 (2014) 1437–1483

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.

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mirror symmetry, mirror theorem
Mathematical Subject Classification 2010
Primary: 14N35
Secondary: 53D45
Received: 5 November 2013
Accepted: 17 January 2014
Published: 7 July 2014
Proposed: Jim Bryan
Seconded: Richard Thomas, Yasha Eliashberg
Yuan-Pin Lee
Department of Mathematics
University of Utah
155 S 1400 E Room 233
Salt Lake City, UT 84112-0090
Mark Shoemaker
Department of Mathematics
University of Utah
155 S 1400 E Room 233
Salt Lake City, UT 84112-0090