We study the moment maps of a smooth projective toric variety. In particular, we characterize when the moment map coming from the quotient construction is equal to a weighted Fubini-Study moment map. This leads to an investigation into polytopes with strict linear precision, and in the process we use results from and find remarkable connections between Symplectic Geometry, Geometric Modeling, Algebraic Statistics, and Algebraic Geometry.

中文翻译：

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矩图、严格线性精度和最大似然度为 1

我们研究平滑投影复曲面变体的矩图。特别是，我们表征了来自商构造的矩图何时等于加权 Fubini-Study 矩图。这导致对具有严格线性精度的多胞体进行研究，在此过程中，我们使用来自辛几何、几何建模、代数统计和代数几何的结果并发现它们之间的显着联系。