## Journal of Differential Geometry

### Double quintic symmetroids, Reye congruences, and their derived equivalence

#### Abstract

Let $\mathscr{Y}$ be the double cover of the quintic symmetric determinantal hypersurface in $\mathbb{P}^{14}$. We consider Calabi–Yau threefolds $Y$ defined as smooth linear sections of $\mathscr{Y}$. In our previous works, we have shown that these Calabi–Yau threefolds $Y$ are naturally paired with Reye congruence Calabi–Yau threefolds $X$ by the projective duality of $\mathscr{Y}$, and observed that these Calabi–Yau threefolds have several interesting properties from the viewpoint of mirror symmetry and also projective geometry. In this paper, we prove the derived equivalence between the linear sections $Y$ of $\mathscr{Y}$ and the corresponding Reye congruences $X$.

#### Article information

Source
J. Differential Geom., Volume 104, Number 3 (2016), 443-497.

Dates
Received: 18 August 2014
First available in Project Euclid: 3 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1478138549

Digital Object Identifier
doi:10.4310/jdg/1478138549

Mathematical Reviews number (MathSciNet)
MR3568628

Zentralblatt MATH identifier
1364.32018

#### Citation

Hosono, Shinobu; Takagi, Hiromichi. Double quintic symmetroids, Reye congruences, and their derived equivalence. J. Differential Geom. 104 (2016), no. 3, 443--497. doi:10.4310/jdg/1478138549. https://projecteuclid.org/euclid.jdg/1478138549