摘要翻译:
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$z_1^{\alpha_1}形式的因子...z_n^{\alpha_n}$其中$\alpha_i$为非零自然整数。如果我们在addicting中假定$F$是最大稀疏多项式(它的支持度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$V_F\子集(\MathBB{C}^*)^N$的$\MathBB{R}^N$中的变形虫$\MathSCR{a}_F$的补分量在$F$的支持度上有序,这意味着$\MathSCR{a}_F$是实的。这对[PR2-01]中的Passare和Rullg\aa的rd问题给出了肯定的回答。
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英文标题:
《Maximally Sparse Polynomials have Solid Amoebas》
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作者:
Mounir Nisse
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Geometric Topology 几何拓扑
分类描述:Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形,轨道,多面体,细胞复合体,叶状,几何结构
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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 $z_1^{\alpha_1}... z_n^{\alpha_n}$ where $\alpha_i$ 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 Rullg\aa rd question in [PR2-01].
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PDF链接:
https://arxiv.org/pdf/0704.2216