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SIGMA, 2012, Volume 8, 047, 7 pages (Mi sigma724)  

This article is cited in 6 scientific papers (total in 6 papers)

Mutations of Laurent polynomials and flat families with toric fibers

Nathan Owen Ilten

Department of Mathematics, University of California, Berkeley CA 94720, USA

Abstract: 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, deformations, Newton polyhedra.

DOI: https://doi.org/10.3842/SIGMA.2012.047

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Full text: http://emis.mi.ras.ru/.../047
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Bibliographic databases:

ArXiv: 1205.4664
MSC: 14M25; 14D06; 53D37
Received: May 21, 2012; in final form July 25, 2012; Published online July 28, 2012
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Citation: Nathan Owen Ilten, “Mutations of Laurent polynomials and flat families with toric fibers”, SIGMA, 8 (2012), 047, 7 pp.

Citation in format AMSBIB
\Bibitem{Ilt12}
\by Nathan Owen Ilten
\paper Mutations of Laurent polynomials and flat families with toric fibers
\jour SIGMA
\yr 2012
\vol 8
\papernumber 047
\totalpages 7
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\crossref{https://doi.org/10.3842/SIGMA.2012.047}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864849875}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Mohammad Akhtar, Tom Coates, Sergey Galkin, Alexander M. Kasprzyk, “Minkowski Polynomials and Mutations”, SIGMA, 8 (2012), 094, 707 pp.  mathnet  crossref
    2. Coates T. Gonshaw S. Kasprzyk A. Nabijou N., “Mutations of Fake Weighted Projective Spaces”, Electron. J. Comb., 21:4 (2014)  mathscinet  zmath  isi
    3. Akhtar M. Coates T. Corti A. Heuberger L. Kasprzyk A. Oneto A. Petracci A. Prince T. Tveiten K., “Mirror Symmetry and the Classification of Orbifold Del Pezzo Surfaces”, Proc. Amer. Math. Soc., 144:2 (2016), 513–527  crossref  mathscinet  zmath  isi  scopus
    4. Akhtar M.E. Kasprzyk A.M., “Mutations of Fake Weighted Projective Planes”, Proc. Edinb. Math. Soc., 59:2 (2016), 271–285  crossref  mathscinet  zmath  isi  elib  scopus
    5. A. Kasprzyk, B. Nill, T. Prince, “Minimality and mutation-equivalence of polygons”, Forum Math. Sigma, 5 (2017), 1–48  crossref  mathscinet  isi
    6. T. Prince, “Smoothing toric fano surfaces using the gross-siebert algorithm”, Proc. London Math. Soc., 117:3 (2018), 617–660  crossref  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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