
SIGMA 8 (2012), 047, 7 pages arXiv:1205.4664
https://doi.org/10.3842/SIGMA.2012.047
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
Abstract
We give a general criterion for two toric varieties to appear as fibers in a flat family over P^{1}.
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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