Mirror symmetry and projective geometry of Reye congruences I

Abstract

Studying the mirror symmetry of a Calabi-Yau threefold $X$ of the Reye congruence in $\mP^4$, we conjecture that $X$ has a non-trivial Fourier-Mukai partner $Y$. We construct $Y$ as the double cover of a determinantal quintic in $\mP^4$ 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.

27 pages, typos corrected, minor changes, to appear in J.Alg.Geom

References in corpus (3)

• Homological projective duality for Grassmannians of lines
• Scheme of lines on a family of 2-dimensional quadrics: geometry and derived category
• Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau threefolds

Cited by in corpus (2)

• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• Duality In Two-Dimensional (2,2) Supersymmetric Non-Abelian Gauge Theories