The mirror quintic as a quintic
Abstract
The general quintic hypersurface in ${\mathbb P}^4$ is the most famous example of a CalabiYau threefold for which mirror symmetry has been investigated in detail. There is a description of the mirror as a hypersurface in a certain weighted projective space. In this note we present a model for the mirror which is again (the resolution of) a quintic hypersurface in ${\mathbb P}^4$. We also deal with the special members in the respective families. They lead to rigid CalabiYau threefolds with interesting arithmetical properties. In the last section we try to find a similarly nice model for the mirror of the complete intersection of two cubics in ${\mathbb P}^5$. We also formulate a general question about mirror models.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2005
 arXiv:
 arXiv:math/0503329
 Bibcode:
 2005math......3329M
 Keywords:

 Algebraic Geometry;
 14J32;
 14G10
 EPrint:
 7 pages