The Hodge structure of semiample hypersurfaces and a generalization of the monomialdivisor mirror map
Abstract
We solved the longstanding problem of describing the cohomology ring of semiample hypersurfaces in complete simplicial toric varieties. Also, the monomialdivisor mirror map is generalized to a map between the whole Picard group and the space of infinitesimal deformations for a mirror pair of CalabiYau 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2000
 arXiv:
 arXiv:math/0012208
 Bibcode:
 2000math.....12208M
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 High Energy Physics  Theory;
 14M25
 EPrint:
 To appear in Advances in Algebraic Geometry Motivated by Physics (ed. E. Previato), Contemporary Mathematics