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Degenerations and mirror contractions of Calabi-Yau complete intersections via Batyrev-Borisov Mirror symmetry

Research paper by Anvar R. Mavlyutov

Indexed on: 24 Feb '11Published on: 24 Feb '11Published in: Mathematics - Algebraic Geometry



Abstract

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-partition corresponds to a Calabi-Yau complete intersection in a Gorenstein Fano toric variety degenerating to an ample Calabi-Yau hypersurface in another Fano toric variety. Using the Batyrev-Borisov mirror symmetry construction, we found the mirror contraction of a Calabi-Yau complete intersection to the mirror of the ample Calabi-Yau hypersurface.