Gaussian likelihood geometry of projective varieties

08/26/2022

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by   Sandra Di Rocco, et al.

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We explore the maximum likelihood degree of a homogeneous polynomial F on a projective variety X, MLD_X(F), which generalizes the concept of Gaussian maximum likelihood degree. We show that MLD_X(F) is equal to the count of critical points of a rational function on X, and give different geometric characterizations of it via topological Euler characteristic, dual varieties, and Chern classes.