Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 047, 7 pages      arXiv:1205.4664
Contribution to the Special Issue “Mirror Symmetry and Related Topics”

Mutations of Laurent Polynomials and Flat Families with Toric Fibers

Nathan Owen Ilten
Department of Mathematics, University of California, Berkeley CA 94720, USA

Received May 21, 2012, in final form July 25, 2012; Published online July 28, 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.

Key words: toric varieties; mirror symmetry; deformations; Newton polyhedra.

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