Duality of Weights, Mirror Symmetry and Arnold's Strange Duality

摘要

A notion of duality of weight systems which corresponds to Batyrev's toricmirror symmetry is given. Explicit duality on the (1,1)-cohomology of K3surfaces which are minimal models of toric hypersurfaces is constructed usingmonomial divisor mirror map of Aspinwall-Greene-Morrison. It is shown thatArnold's strange duality for exceptional unimodal singularities reduces to thisduality.