Deformations of Calabi-Yau hypersurfaces arising from deformations of toric varieties

There are easy “polynomial” deformations of Calabi-Yau hypersurfaces in toric varieties performed by changing the coefficients of the defining polynomial of the hypersurface. In this paper, we explicitly constructed the ``non-polynomial’’ deformations of Calabi-Yau hypersurfaces, which arise from deformations of the ambient toric variety.