Mirror symmetry and projective geometry of Reye congruences I

2011/01/14 by Shinobu Hosono, Hosono, Shinobu, Hiromichi Takagi +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1101.2746

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

openalex publication_date 2011/01/14 · arxiv created 2012/07/02 · arxiv updated 2012/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Studying the mirror symmetry of a Calabi-Yau threefold X of the Reye congruence in \mP⁴, we conjecture that X has a non-trivial Fourier-Mukai partner Y. We construct Y as the double cover of a determinantal quintic in \mP⁴ branched over a curve. We also calculate BPS numbers of both X and Y (and also a related Calabi-Yau complete intersection X₀) using mirror symmetry.

Citations

• Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau threefolds
• The Pfaffian Calabi-Yau, its Mirror, and their link to the Grassmannian G(2,7)
• M-Theory and Topological Strings--II

Cited by

• A single point as a Calabi-Yau zerofold

Related

• Determinantal Quintics and Mirror Symmetry of Reye Congruences
• Double quintic symmetroids, Reye congruences, and their derived equivalence
• Mirror Symmetry and Projective Geometry of Fourier-Mukai Partners
• The mirror quintic as a quintic
• Geometric Aspects of Mirror Symmetry