阿米巴轮廓的稀疏界
Sparse Bounds for Amoeba Contours
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中文总结 AI 辅助
该研究推导代数曲线和超曲面的阿米巴轮廓实次数新上界，改进Lang--Shapiro--Shustin的普法夫方法，采用对数余法向消除等技术，为洛朗多项式类得出通用界和更精确稀疏估计，通过实例展示新界优于已知估计。
中文摘要 AI 辅助
我们推导了代数曲线和超曲面的阿米巴轮廓实次数的新上界。我们的方法改进了Lang--Shapiro--Shustin的普法夫方法，通过用对数余法向消除和基于变换牛顿多面体的稀疏混合体积技术取代大的总次数估计。这为广泛的洛朗多项式类产生了通用界以及明显更精确的稀疏估计。通过比较和具体例子说明了新界相对于先前已知通用估计的改进。
英文摘要
We derive new upper bounds for the real degree of the contour of the amoeba of algebraic curves and hypersurfaces. Our approach refines the Pfaffian method of Lang--Shapiro--Shustin by replacing large total-degree estimates with logarithmic-conormal elimination and sparse mixed-volume techniques based on the transformed Newton polytopes. This yields universal bounds together with significantly sharper sparse estimates for broad classes of Laurent polynomials. Several comparisons and explicit examples illustrate the improvement of the new bounds over the previously known universal estimates.
