Double quintic symmetroids, Reye congruences, and their derived equivalence

2013/02/24 by Shinobu Hosono, Hosono, Shinobu, Hiromichi Takagi +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1302.5883

46 pages, 2 figures

arxiv created 2013/11/08 · arxiv updated 2013/11/11

Abstract

We consider Calabi-Yau threefolds Y defined as smooth linear sections of the double cover of the quintic symmetric determinantal hypersurface in P¹⁴. In our previous works, we have shown that these Calabi-Yau threefolds Y are naturally paired with Reye congruence Calabi-Yau threefolds X, and X and Y have several interesting properties from the view point of mirror symmetry and projective geometry. In this paper, we prove the derived equivalence between Y and X.

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