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Embedding of Calabi-Yau deformations into toric varieties
Anvar R. Mavlyutov
We show that "non-polynomial" deformations of semiample (minimal) nondegenerate Calabi-Yau hypersurfaces in complete simplicial toric varieties can be realized as quasismooth compl…
String cohomology of Calabi-Yau hypersurfaces via Mirror Symmetry
Lev A. Borisov, Anvar R. Mavlyutov
We propose a construction of string cohomology spaces for Calabi-Yau hypersurfaces that arise in Batyrev's mirror symmetry construction. The spaces are defined explicitly in terms…
The Hodge structure of semiample hypersurfaces and a generalization of the monomial-divisor mirror map
Anvar R. Mavlyutov
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 ge…
On the chiral ring of Calabi-Yau hypersurfaces in toric varieties
Anvar R. Mavlyutov
We study the B-model chiral ring of Calabi-Yau hypersurfaces in Batyrev's mirror construction. The main result is an explicit description of a subring of the chiral ring of semiamp…
Semiample hypersurfaces in toric varieties
Anvar R. Mavlyutov
We study the geometry and cohomology of semiample hypersurfaces in toric varieties. Such hypersurfaces generalize the MPCP-desingularizations of Calabi-Yau ample hypersurfaces in t…