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Almost-toric hypersurfaces

Abstract

An almost-toric hypersurface is parameterized by monomials multiplied by polynomials in one extra variable. We determine the Newton polytope of such a hypersurface, and apply this to give an algorithm for computing the implicit polynomial equation.

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Author information

Correspondence to Bo Lin.

Additional information

The author thanks Bernd Sturmfels for his guidance, Ralph Morrison for his insightful suggestions and Nathan Ilten for discussions. This work was supported by the Thematic Program of National Institute for Mathematical Sciences, Daejeon, Korea, which hosted the author in the summer of 2014.

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Lin, B. Almost-toric hypersurfaces. Beitr Algebra Geom 57, 343–359 (2016). https://doi.org/10.1007/s13366-015-0268-0

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Keywords

  • Toric variety
  • Tropical geometry
  • Almost-toric

Mathematics Subject Classification

  • Primary 14J70
  • Secondary 14T05