22 citations · 63 across the 12 of their papers we have counts for
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Mirror Symmetry for Calabi-Yau complete intersections in Fano toric varieties
Anvar R. Mavlyutov
Generalizing the notions of reflexive polytopes and nef-partitions of Batyrev and Borisov, we propose a mirror symmetry construction for Calabi-Yau complete intersections in Fano t…
Degenerations and mirror contractions of Calabi-Yau complete intersections via Batyrev-Borisov Mirror symmetry
Anvar R. Mavlyutov
We show that the dual of the Cayley cone, associated to a Minkowski sum decomposition of a reflexive polytope, contains a reflexive polytope admitting a nef-partition. This nef-par…
Deformations of Toric Varieties via Minkowski Sum Decompositions of Polyhedral Complexes
Anvar Mavlyutov
We generalized the construction of deformations of affine toric varieties of K. Altmann and our previous construction of deformations of weak Fano toric varieties to the case of ar…
Cohomology of rational forms and a vanishing theorem on toric varieties
Anvar Mavlyutov
We explicitly describe cohomology of the sheaf of differential forms with poles along a semiample divisor on a complete simplicial toric variety. As an application, we obtain a new…
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…
Deformations of Calabi-Yau hypersurfaces arising from deformations of toric varieties
Anvar R. Mavlyutov
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 th…