A mirror duality for families of \(K3\) surfaces associated to bimodular singularities (Q5965198)

\textit{M. Mase} and \textit{K. Ueda} [Manuscr. Math. 146, No. 1--2, 153--177 (2015; Zbl 1405.14104)] proved the polytope mirror symmetry for families of \(K3\) surfaces associated to bimodular singularites. In this article, the author tries to extend the polytope mirror symmetry to lattice mirror symmetry of \(K3\) surfaces in the sense of \textit{I. V. Dolgachev} [J. Math. Sci., New York 81, No. 3, 2599--2630 (1996; Zbl 0890.14024)]. The main result is that for six specific polytope mirror pairs, the lattice mirror symmetry holds. The Picard number takes values in the set \(\{2,3,4\}\). This method used in the proof is to give relations between toric geometry and lattice theory, in particular, via the intersection matrices of toric divisors and lattices.