The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map

Details The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map

2000-12-20

arxiv.org/abs/math/0012208v1

Mathematics

Algebraic Geometry

To appear in Advances in Algebraic Geometry Motivated by Physics (ed. E. Previato), Contemporary Mathematics

Scientific paper

We 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.

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