Mirror symmetry and projective geometry of Reye congruences I

TL;DR

This paper explores mirror symmetry for a specific Calabi-Yau threefold of Reye congruence, proposing a Fourier-Mukai partner and computing BPS numbers for both, advancing understanding of their geometric and physical properties.

Contribution

It conjectures a new Fourier-Mukai partner for the Reye congruence Calabi-Yau and constructs it explicitly as a double cover, also calculating BPS invariants via mirror symmetry.

Findings

Conjecture of a non-trivial Fourier-Mukai partner for the Reye congruence Calabi-Yau.

Explicit construction of the partner as a double cover of a determinantal quintic.

Calculation of BPS numbers for the Calabi-Yau and its partner.

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.