Mutations of Laurent Polynomials and Flat Families with Toric Fibers - Ilten, N.O. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
We give a general criterion for two toric varieties to appear as fibers in a flat family over P¹. We apply this to show that certain birational transformations mapping a Laurent polynomial to another Laurent polynomial correspond to deformations between the associated toric varieties.