Moment Maps, Strict Linear Precision, and Maximum Likelihood Degree One
Patrick Clarke, David A. Cox
TL;DR
This paper explores the conditions under which moment maps of smooth projective toric varieties align with weighted Fubini-Study maps, revealing deep links between geometry, modeling, and statistics.
Contribution
It characterizes when the moment map equals a weighted Fubini-Study map and investigates polytopes with strict linear precision, connecting multiple mathematical disciplines.
Findings
Characterization of when the moment map equals a weighted Fubini-Study map
Identification of polytopes with strict linear precision
Establishment of connections between symplectic geometry, modeling, and algebraic statistics
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.
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