Mutations of Laurent Polynomials and Flat Families with Toric Fibers

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2012
• Main Author: Ilten, N.O.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2012
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148435
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Mutations of Laurent Polynomials and Flat Families with Toric Fibers / N.O. Ilten // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 6 назв. — англ.

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.