具有实变形虫的极大稀疏多项式
Maximally Sparse Polynomials have Solid Amoebas
摘要：
设$f$是$\mathbb{C}[z_1,..., z_n]$中的一个普通多项式，没有负指数，也没有$z_1^{α_1}... z_n^{α_n}$形式的因子，其中$α_i$是非零自然整数。如果我们在addition中假设$f$是最大稀疏多项式（它的支集等于它的牛顿多面体的顶点集），那么由$f$定义的代数超曲面$V_f\subset (\mathbb{C}^*)^n$的$\mathbb{R}^n$中的变形虫$\mathscr{A}_f$的补分量具有位于$f$的支集中的阶，这意味着$\mathscr{A}_f$是实心的。这对[PR 2 -01]中的Passare和Rullgård问题给出了肯定的回答。
英文摘要：
Let $f$ be an ordinary polynomial in $\mathbb{C}[z_1,..., z_n]$ with no negative exponents and with no factor of the form $z_1^{α_1}... z_n^{α_n}$ where $α_i$ are non zero natural integer. If we assume in addicting that $f$ is maximally sparse polynomial (that its support is equal to the set of vertices of its Newton polytope), then a complement component of the amoeba $\mathscr{A}_f$ in $\mathbb{R}^n$ of the algebraic hypersurface $V_f\subset (\mathbb{C}^*)^n$ defined by $f$, has order lying in the support of $f$, which means that $\mathscr{A}_f$ is solid. This gives an affirmative answer to Passare and Rullgård question in [PR2-01].
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