Mirror symmetry for double cover Calabi–Yau varieties

The presented paper is a continuation of the series of papers https: //academic. oup. com/imrn/advance-article-pdf/doi/10. 1093/imrn/rnz259/30788308/rnz259. pdf17, https: //dx. doi. org/10. 4310/CNTP. 2020. v14. n4. a218. In this paper, utilizing Batyrev and Borisov's duality construction on nef‑partitions, we generalize the recipe in https: //academic. oup. com/imrn/advance-article-pdf/doi/10. 1093/imrn/rnz259/30788308/rnz259. pdf17, https: //dx. doi. org/10. 4310/CNTP. 2020. v14. n4. a218 to construct a pair of singular double cover Calabi–Yau varieties (Y, Y^) over toric manifolds and compute their topological Euler characteristics and Hodge numbers. In the 3-dimensional cases, we show that (Y, Y^) forms a topological mirror pair, i. e. , h^p, q (Y) = h^3-p, q (Y^) for all p, q.