Equivalences of families of stacky toric Calabi-Yau hypersurfaces

18 May 2018

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 quartics in $\mathbb{P}^3$, and a birational reduction of Reid’s list to 81 families.