Equivalences of Families of Stacky Toric Calabi-Yau Hypersurfaces

2015/03/17 by Doran, Charles F., Favero, David, Kelly, Tyler L.
#14J28 #14J32 #14J33 #14M25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.04888

Abstract

Given the same anti-canonical linear system on two distinct toric varieties, we provide a derived equivalence between partial crepant resolutions of the corresponding stacky hypersurfaces. The applications include: a derived unification of toric mirror constructions, calculations of Picard lattices for linear systems of quartic surfaces, and a birational reduction of Reid's list to 81 families.

Related

• Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties
• Toric Representation and Positive Cone of Picard Group and Deformation Space in Mirror Symmetry of Calabi-Yau Hypersurfaces in Toric Varieties
• Families of Calabi-Yau hypersurfaces in \mathbb Q-Fano toric varieties
• Some examples of Calabi-Yau pairs with maximal intersection and no toric model
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties