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Moment maps, strict linear precision, and maximum likelihood degree one

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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… Click to show full abstract

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.

Keywords: moment; strict linear; moment maps; linear precision; geometry

Journal Title: Advances in Mathematics
Year Published: 2020

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