2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60628We solved the long-standing problem of describing the cohomology ring of semiample hypersurfaces in complete simplicial toric varieties. Also, the monomial-divisor mirror map is generalized to a map between the whole Picard group and the space of infinitesimal deformations for a mirror pair of Calabi-Yau hypersurfaces. This map is compatible with certain vanishing limiting products of the subrings of the chiral rings, on which the ring structure is related to a product of the roots of $A$-type Lie algebra.To appear in Advances in Algebraic Geometry Motivated by Physics (ed. E. Previato), Contemporary MathematicsAlgebraic GeometryHigh Energy Physics - TheoryMathematical Physics14M25text