Geodesic
Mutations of Laurent polynomials and flat families with toric fibers
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a general criterion for two toric varieties to appear as fibers in a flat family over $\mathbb P^1$. 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.
Keywords: toric varieties, mirror symmetry, Newton polyhedra.
Mots-clés : deformations 
@article{SIGMA_2012_8_a46,
     author = {Nathan Owen Ilten},
     title = {Mutations of {Laurent} polynomials and flat families with toric fibers},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2012},
     volume = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a46/}
}
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Nathan Owen Ilten. Mutations of Laurent polynomials and flat families with toric fibers. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a46/

[1] Altmann K., Hausen J., “Polyhedral divisors and algebraic torus actions”, Math. Ann., 334 (2006), 557–607 ; arXiv: math.AG/0306285 | DOI | MR | Zbl

[2] Auroux D., “Mirror symmetry and $T$-duality in the complement of an anticanonical divisor”, J. Gökova Geom. Topol. GGT, 1 (2007), 51–91 ; arXiv: 0706.3207 | MR | Zbl

[3] Fulton W., Introduction to toric varieties, Annals of Mathematics Studies, 131, Princeton University Press, Princeton, NJ, 1993 | MR | Zbl

[4] Galkin S., Usnich A., Mutations of potentials, Preprint IPMU 10-0100

[5] Ilten N.O., Vollmert R., “Deformations of rational $T$-varieties”, J. Algebraic Geom., 21 (2012), 531–562 ; arXiv: 0903.1393 | DOI | Zbl

[6] Mavlyutov A., Deformations of toric varieties via Minkowski sum decompositions of polyhedral complexes, arXiv: 0902.0967