对数Voronoi单元的边界可以是超越的
Boundaries of logarithmic Voronoi cells can be transcendental
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中文总结 AI 辅助
该研究证明概率单形中一维代数模型的对数Voronoi边界未必是代数的，通过两条直线并集和尖点曲线的两个例子佐证了这一结论。
中文摘要 AI 辅助
我们证明，概率单形中一维代数模型的对数Voronoi边界未必是代数的，给出两个明确例子：对于两条直线的并集，特定光滑有理点处的对数Voronoi单元有一个超越边界点；对于尖点曲线，奇异点处的单元包含一条非代数实解析边界分支。
英文摘要
We show that logarithmic Voronoi boundaries for one-dimensional algebraic models in the probability simplex need not be algebraic. We give two explicit examples. For a union of two lines, the logarithmic Voronoi cell at a specific smooth rational point has a transcendental boundary point. For a cuspidal curve, the cell at the singular point contains a non-algebraic real-analytic boundary branch.
