2025/10/07 by Tsung-Ju Lee, Lee, Tsung-Ju, Bong H. Lian +3
Mathematics · #14D07 #14J33 #14N35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2510.05470
openalex publication_date 2025/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue our study on the pairs of singular Calabi--Yau varieties arising from double covers over semi-Fano toric manifolds. In this paper, we first investigate singular CY double covers of \(ℙ3\) branched along (1) a union of eight hyperplanes in general position, and (2) a union of four hyperplanes and a quartic in generation. Our previous construction produces hypothetical singular mirror partners. We prove that they are mirror pairs in the sense that the \(B\)-model of one (variation of Hodge structure) is equivalent to the \(A\)-model of another (the untwisted part of the genus zero orbifold Gromov--Witten invariants). The technique can be generalized and applied to the case when the nef-partition is trivial. As a byproduct, we also verify Morrison's conjecture in certain circumstances.