English

Amoeba finite basis of solutions to a system of $n$ polynomials in $n$ variables

Algebraic Geometry 2014-04-15 v1

Abstract

We show that the amoeba of a complex algebraic variety defined as the solutions to a generic system of nn polynomials in nn variables has a finite basis. In other words, it is the intersection of finitely many hypersurface amoebas. Moreover, we give an upper bound of the size of the basis in terms of nn and the mixed volume μ\mu of the Newton polytopes of the polynomial equations of the system. Also, we give an upper bound of the degree of the basis elements in terms of μ\mu.

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Cite

@article{arxiv.1404.3593,
  title  = {Amoeba finite basis of solutions to a system of $n$ polynomials in $n$ variables},
  author = {Mounir Nisse},
  journal= {arXiv preprint arXiv:1404.3593},
  year   = {2014}
}

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5 pages