Lattice duality for families of $K3$ surfaces associated to transpose duality

Abstract

The aim of this article is to show that the transpose-dual pairs in the sense of Ebeling-Ploog of singularities $(Z_{1,0},Z_{1,0})$, $(U_{1,0},U_{1,0})$, $(Q_{17},Z_{2,0})$, $(W_{1,0},W_{1,0})$ that are concluded to be polytope-dual by the author are actually lattice-dual.

arXiv comment16 pages,3 tables,to appear in manuscripta mathematica