Mirror symmetry and projective geometry of Reye congruences I

Hosono, Shinobu; Takagi, Hiromichi

doi:10.1090/S1056-3911-2013-00618-9

Authors: Shinobu Hosono and Hiromichi Takagi
Journal: J. Algebraic Geom. 23 (2014), 279-312
DOI: https://doi.org/10.1090/S1056-3911-2013-00618-9
Published electronically: July 15, 2013
MathSciNet review: 3166392
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Abstract | References | Additional Information

Abstract: Studying the mirror symmetry of a Calabi-Yau threefold $X$ of the Reye congruence in $\mathbb {P}^4$, we conjecture that $X$ has a non-trivial Fourier-Mukai partner $Y$. We construct $Y$ as the double cover of a determinantal quintic in $\mathbb {P}^4$ branched over a curve. We also calculate BPS numbers of both $X$ and $Y$ (and also a related Calabi-Yau complete intersection $\tilde X_0$) using mirror symmetry.

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Additional Information

Shinobu Hosono
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguro-ku, Tokyo 153-8914, Japan
Email: hosono@ms.u-tokyo.ac.jp

Hiromichi Takagi
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguro-ku, Tokyo 153-8914, Japan
Email: takagi@ms.u-tokyo.ac.jp

Received by editor(s): February 7, 2011
Received by editor(s) in revised form: June 4, 2012
Published electronically: July 15, 2013
Additional Notes: The first author was supported in part by Grant-in-Aid for Scientific Research, C 18540014. The second author was supported in part by Grant-in-Aid for Young Scientists, B 20740005
Article copyright: © Copyright 2013 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.