Maximally Sparse Polynomials Have Solid Amoebas
نویسندگان
چکیده
Let f be an ordinary polynomial in C[z1, . . . , zn] with no negative exponents and with no factor of the form z1 1 . . . z αn n where αi are non zero natural integers. If we assume in addition that f is a maximally sparse polynomial (that its support is equal to the set of vertices of its Newton polytope), then a complement component of the amoeba Af in R of the algebraic hypersurface Vf ⊂ (C∗)n de ned by f , has order lying in the support of f , which means that Af is solid. This gives an a rmative answer to Passare and Rullgård question in [PR2-01].
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